NEW Scene Study
NEW Scene Study

My PLUS

  • Literature
  • Shakespeare
  • Other Subjects
  • AP® Test Prep PLUS dark gray
  • Teacher dark gray
    • SparkTeach
    • Teacher's Handbook
  • Blog
My PLUS Dashboard
  • My PLUS Activity dark gray
    • Notes
    • Bookmarks
    • Test Prep PLUS
    • No Fear Translations & Audio
    • Mastery Quizzes
    • Flashcards
    • Infographics
    • No Fear Graphic Novels
  • Account Details
  • Subscription & Billing
  • Manage Group Discount

Please wait while we process your payment

Reset Password

  • Please wait while we process your payment

    Get instant, ad-free access to our grade-boosting study tools with a 7-day free trial!

    Learn more

    space-cat-group

    spark-notes-logo

    Sign up Log in
    step1

    Create Account

    Continue with Google

    or email

    Looks like an account already exists for this email address! Please sign in, or create a new account with a different email address.

    Email

    Please use a valid email address

    Password

    Your password must:
    •   Be between 8-15 characters.
    •   Contain at least one capital letter.
    •   Contain at least one number.
    •   Be different from your email address.
    eye-icon cross-eye-icon

    Sorry, this password doesn't meet our criteria. Please check the password tip above and try again.

    By signing up, I confirm that I or my legal guardian has read the Privacy Policy and agrees to the Terms of Service.

    Already have an account? Log in

    This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.

    Log into your PLUS account

    Continue with Google

    or email

    Please enter your email and password.

    .

    Email

    Please use a valid email address

    Password

    Your password must:
    •   Be between 8-15 characters.
    •   Contain at least one capital letter.
    •   Contain at least one number.
    •   Be different from your email address.
    eye-icon cross-eye-icon

    Sorry, this password doesn't meet our criteria. Please check the password tip above and try again.

    Forgot Password?

    Don’t have an account? Sign up

    Create Account

    2

    Select Plan

    3

    Payment Info

    4

    Start 7-Day Free Trial!

    Select Your Plan

    Individual
    Group Discount

    Monthly

    $5.99

    /month + tax

    Annual

    $29.99

    /year + tax

    Annual

    2-49 accounts

    $22.49/year + tax

    SAVE 25%

    50-99 accounts

    $20.99/year + tax

    SAVE 30%

    Select Quantity

    Price per seat

    $29.99 $--.--

    Subtotal

    $-.--

    Select Annual Plan

    Want 100 or more? Request a customized plan

    What’s Included in the Plans?

    Monthly

    $5.99

    /month + tax

    You could save over 50%

    by choosing an Annual Plan!

    Annual

    $29.99

    /year + tax

    SAVE OVER 50%

    compared to the monthly price!

    Focused-studying
    AD Free IconAd-free experience Check Mark Icon Check Mark Icon
    Study Guide IconStudy Guides for 1,000+ titles Check Mark Icon Check Mark Icon
    Full Text IconFull Text content for 250+ titles Check Mark Icon Check Mark Icon
    PLUS Study Tools
    No Fear IconNo Fear Translations of Shakespeare’s plays (along with audio!) and other classic works Check Mark Icon Check Mark Icon
    Flashcards IconFlashcards Check Mark Icon Check Mark Icon
    Mastery Quizzes IconMastery Quizzes Check Mark Icon Check Mark Icon
    Infographics IconInfographics Check Mark Icon Check Mark Icon
    Graphic Novels IconGraphic Novels Check Mark Icon Check Mark Icon
    AP® Test Prep PLUS
    AP Test Prep IconAP® Practice & Lessons Check Mark Icon Check Mark Icon
    My PLUS Activity
    AP Test Prep IconNote-taking Check Mark Icon Check Mark Icon
    AP Test Prep IconBookmarking Check Mark Icon Check Mark Icon
    AP Test Prep IconDashboard Check Mark Icon Check Mark Icon

    Annual

    $22.49/month + tax

    Save 25%

    on 2-49 accounts

    Annual

    $20.99/month + tax

    Save 30%

    on 50-99 accounts

    Focused-studying
    AD Free IconAd-free experience Check Mark Icon Check Mark Icon
    Study Guide IconStudy Guides for 1,000+ titles Check Mark Icon Check Mark Icon
    Full Text IconFull Text content for 250+ titles Check Mark Icon Check Mark Icon
    PLUS Study Tools
    No Fear IconNo Fear Translations of Shakespeare’s plays (along with audio!) and other classic works Check Mark Icon Check Mark Icon
    Flashcards IconFlashcards Check Mark Icon Check Mark Icon
    Mastery Quizzes IconMastery Quizzes Check Mark Icon Check Mark Icon
    Infographics IconInfographics Check Mark Icon Check Mark Icon
    Graphic Novels IconGraphic Novels Check Mark Icon Check Mark Icon
    AP® Test Prep PLUS
    AP Test Prep IconAP® Practice & Lessons Check Mark Icon Check Mark Icon
    My PLUS Activity
    AP Test Prep IconNote-taking Check Mark Icon Check Mark Icon
    AP Test Prep IconBookmarking Check Mark Icon Check Mark Icon
    AP Test Prep IconDashboard Check Mark Icon Check Mark Icon

    Testimonials from SparkNotes Customers

    icon-plus-quotes

    No Fear provides access to Shakespeare for students who normally couldn’t (or wouldn’t) read his plays. It’s also a very useful tool when trying to explain Shakespeare’s wordplay!

    icon-testimonial-erika

    Erika M.

    icon-plus-quotes

    I tutor high school students in a variety of subjects. Having access to the literature translations helps me to stay informed about the various assignments. Your summaries and translations are invaluable.

    icon-testimonial-erika

    Kathy B.

    icon-plus-quotes

    Teaching Shakespeare to today's generation can be challenging. No Fear helps a ton with understanding the crux of the text.

    icon-testimonial-erika

    Kay H.

    Testimonials from SparkNotes Customers

    icon-plus-quotes

    No Fear provides access to Shakespeare for students who normally couldn’t (or wouldn’t) read his plays. It’s also a very useful tool when trying to explain Shakespeare’s wordplay!

    icon-testimonial-erika

    Erika M.

    icon-plus-quotes

    I tutor high school students in a variety of subjects. Having access to the literature translations helps me to stay informed about the various assignments. Your summaries and translations are invaluable.

    icon-testimonial-erika

    Kathy B.

    icon-plus-quotes

    Teaching Shakespeare to today's generation can be challenging. No Fear helps a ton with understanding the crux of the text.

    icon-testimonial-erika

    Kay H.

    Create Account

    Select Plan

    3

    Payment Info

    4

    Start 7-Day Free Trial!

    Payment Information

    You will only be charged after the completion of the 7-day free trial.

    If you cancel your account before the free trial is over, you will not be charged.

    You will only be charged after the completion of the 7-day free trial. If you cancel your account before the free trial is over, you will not be charged.

    Order Summary

    Annual

    7-day Free Trial

    SparkNotes PLUS

    $29.99 / year

    Annual

    Quantity

    51

    PLUS Group Discount

    $29.99 $29.99 / seat

    Tax

    $0.00

    SPARK25

    -$1.25

    25% Off

    Total billed on Nov 7, 2024 after 7-day free trail

    $29.99

    Total billed

    $0.00

    Due Today

    $0.00

    Promo code

    This is not a valid promo code

    Card Details

    By placing your order you agree to our terms of service and privacy policy.

    By saving your payment information you allow SparkNotes to charge you for future payments in accordance with their terms.

    Powered by stripe

    Legal

    Google pay.......

    snplus logo
    Welcome to snplus logo snplus logo thumb icon

    Thank You!

    Your group members can use the joining link below to redeem their membership. They will be prompted to log into an existing account or to create a new account. All members under 16 will be required to obtain a parent's consent sent via link in an email.

    Your Child’s Free Trial Starts Now!

    Thank you for completing the sign-up process. Your child’s SparkNotes PLUS login credentials are [email] and the associated password. If you have any questions, please visit our help center.

    Your Free Trial Starts Now!

    Please wait while we process your payment

    snplus-logo

    Parent’s Email is Required
    A parent must help manage your account. Enter their email below and we’ll send them a link to finish signing up for SparkNotes PLUS.
    Parent’s email address

    Sorry, you must enter a valid email address

    By entering an email, you agree to our privacy policy.

    Please wait while we process your payment

    snplus-logo

    Email Sent Parent’s Email is Required
    We’ve sent an email to parentsname@email.com. In order to access SparkNotes PLUS, your parent must click the link provided in the email. We’ve sent an email to parentsname@email.com. In order to access SparkNotes PLUS, your parent must follow the link provided in the email to complete the sign-up process.

    Sorry, you must enter a valid email address

    By entering an email, you agree to our privacy policy.

    • Literature
    • Shakespeare
    • Other Subjects
    • AP® Test Prep PLUS
    • Teacher
      • SparkTeach
      • Teacher's Handbook
    • Blog
    • Help
      • My  PLUS  Activity
        • Notes
        • Bookmarks
        • AP® Test Prep PLUS
        • No Fear Translations & Audio
        • Mastery Quizzes
        • Flashcards
        • Infographics
        • No Fear Graphic Novels
    • Account Details
    • Subscription & Billing
    • Manage Group Discount

    Please wait while we process your payment

    expired-logo

    Your PLUS subscription has expired

    • We’d love to have you back! Renew your subscription to regain access to all of our exclusive, ad-free study tools.
    • Renew your subscription to regain access to all of our exclusive, ad-free study tools.
    Renew your subscription

    Please wait while we process your payment

    expired-logo

    snpromo-logo
    • Go ad-free AND get instant access to grade-boosting study tools!  

    Geometric Surfaces

    Math

    • Title Home
    • Study Guide
    • Topics
      • Geometric Surfaces
      • Three Dimensions
      • Problems
      • Prisms and Cylinders
      • Problems
      • Pyramids and Cones
      • Problems
      • Regular Polyhedra and Spheres
      • Problems
    • Terms

    Please wait while we process your payment

    snplus-logo

    Unlock your FREE SparkNotes PLUS trial!

    Unlock your FREE Trial!

    Sign up and get instant access to bookmarks.
    • Ad-Free experience
    • Easy-to-access study notes
    • Flashcards & Quizzes
    • AP® English test prep
    • Plus much more
    Already have an account? Log in

    Geometric Surfaces Terms

    Terms

    Geometric Surfaces Terms
    • Altitude of a Cone

      The segment with one endpoint at the vertex of a cone and the other in the plane that contains the base of the cone.

    • Altitude of a Pyramid

      The segment with one endpoint at the vertex of a pyramid and the other at the center of the base of the pyramid.

    • Base of a Cone

      The simple closed curve that bounds part of the cone.

    • Base of a Cylinder

      One of two simple closed curves that lie in parallel planes.

    • Base of a Prism

      One of two polygons that lie in parallel planes.

    • Base of a Pyramid

      A polygon that bounds part of the pyramid.

    • Center of a Sphere

      The fixed point in the interior of a sphere from which all points on the sphere are equidistant

    • Circular Cone

      A cone whose base is a circle

    • Circular Cylinder

      A cylinder whose base is a circle.

    • Concave Simple Closed Surface

      A simple closed surface in which one or more segments* drawn between points on the surface lie partially or wholly outside the surface.

    • Concentric Spheres

      Spheres that share a common center.

    • Cone

      A surface that includes a simple closed curve and the segments that join all the points on that curve with a single fixed point not in the plane of the curve.

    • Convex Simple Closed Surface

      A simple closed curve in which a segment joining any two points on the surface lies entirely in the interior of the surface.

    • Cube

      A regular polyhedron with six faces, all of which are congruent squares.

    • Cylinder

      A geometric surface composed of two congruent simple closed curves lying in parallel planes and segments of parallel lines joining the curves.

    • Dodecahedron

      A twelve-faced regular polyhedron whose faces are all congruent regular pentagons.

    • Edge

      The intersection of two polygons in a polyhedron.

    • Face

      A polygon in a polyhedron.

    • Geometric Solid

      A region in space bounded by a closed surface.

    • Hemisphere

      Exactly half of a sphere.

    • Isocahedron

      A twenty-faced regular polyhedron whose faces are all congruent triangles.

    • Lateral Edge

      An edge of a polyhedron, usually refers to a prism or a pyramid.

    • Lateral Face of a Prism

      The parallelograms of a prism whose edges are the segments that connect the bases.

    • Lateral Face of a Pyramid

      The triangles of a pyramid.

    • Lateral Surface of a Cone

      The set of segments that join the base of a cone with its vertex.

    • Lateral Surface of a Cylinder

      The set of segments that join the bases of a cylinder.

    • Octahedron

      An eight-faced regular polyhedron whose faces are all congruent triangles.

    • Polyhedron

      A simple closed surface composed of regions of intersecting planes--these regions are polygons

    • Prism

      A polyhedron composed of two congruent polygons that lie in parallel planes and the segments that are part of parallel lines that join the congruent polygons.

    • Pyramid

      A polyhedron composed of a polygon and the segments that join that polygon with a fixed point not in the plane of the polygon.

    • Radius of a Sphere

      A segment with one endpoint at the center of a sphere and the other endpoint on the sphere.

    • Regular Polyhedron

      A polyhedron whose faces are congruent regular polygons

    • Regular Pyramid

      A pyramid whose base is a regular polygon and whose altitude intersects the plane of its base at the center of the base.

    • Right Circular Cone

      A circular cone whose altitude intersects with the plane of the base at the center of the base.

    • Right Circular Cylinder

      A circular cylinder whose lateral edges are perpendicular to the planes that contain the bases.

    • Right Prism

      A prism whose lateral edges are perpendicular to the planes of the bases.

    • Simple Closed Surface

      A surface that divides space into three distinct regions: 1) points in the interior of the surface, which always form the endpoints of finite segments; 2) points on the surface; and 3) points in the exterior of the surface, which can form the endpoints of infinite segments.

    • Sphere

      A surface whose points all lie an equal distance from a fixed point in space.

    • Surface

      A geometric figure that traces the motion of a curve in space. A surface is two-dimensional, but can span three dimensions.

    • Tetrahedron

      A four-faced regular polyhedron whose faces are all congruent triangles.

    • Vertex of a Cone

      The fixed point that is the endpoint of all the segments that form the lateral surface of a cone.

    • Vertex of a Polyhedron

      Any point on a polyhedron that is the intersection of three or more faces.

    • Vertex of a Pyramid

      The fixed point at the intersection of all the faces of the pyramid.

    Did you know you can highlight text to take a note? x

    Please wait while we process your payment

    snplus-logo

    Unlock your FREE SparkNotes PLUS trial!

    Unlock your FREE Trial!

    Sign up and get instant access to creating and saving your own notes as you read.
    • Ad-Free experience
    • Easy-to-access study notes
    • Flashcards & Quizzes
    • AP® English test prep
    • Plus much more
    Already have an account? Log in

    Take a Study Break

    • The 7 Most Messed-Up Short Stories We All Had to Read in School

    • 18 of the Most Brilliant Lines of Foreshadowing in Literature

    • QUIZ: Is This a Taylor Swift Lyric or a Quote by Edgar Allan Poe?

    • QUIZ: Which Greek God Are You?

    Sign up for our latest news and updates!
    By entering your email address you agree to receive emails from SparkNotes and verify that you are over the age of 13. You can view our Privacy Policy here. Unsubscribe from our emails at any time.

    SparkNotes—the stress-free way to a better GPA

    • Explore
    • Literature
    • Shakespeare
    • Other Subjects
    • AP® Test Prep PLUS
    • Teacher’s Handbook
    • Blog
    • Premium Study Tools
    • SparkNotes PLUS
    • Sign Up
    • Log In
    • PLUS Help
    • Helpful Resources
    • How to Cite SparkNotes
    • How to Write Literary Analysis
    • William Shakespeare's Life & Times
    • Glossary of Shakespeare Terms
    • Glossary of Literary Terms
    • About Us
    • Help
    • About
    • Contact Us

    Copyright © SparkNotes LLC

    • Terms of Use
    • |
    • Privacy
    • |
    • Cookie Policy
    • |
    • Your Privacy Choices