**Problem : **
Apply the disk method to find the volume of the unit sphere obtained by revolving the
region below the graph of *f* (*x*) = from *x* = - 1 to 1 about the *x*-axis.

Π()^{2}dx | = | Π(1 - x^{2})dx | |

= | Π - | ||

= |

as expected.

**Problem : **
Apply the shell method to find the volume of the solid obtained by revolving the region
below the graph of *f* (*x*) = *x*^{2} from *x* = 0 to 1 about the *y*-axis (this solid looks
like a cylinder with a bowl carved out of the top).

2Πx(x^{2})dx | = | 2Πx^{3}dx | |

= | 2Π|_{0}^{1} | ||

= |

**Problem : **
Compute the volume of the square pyramid with base in the *x* = 0 plane with sides of
length 10 and vertex at the point (5, 0), using the cross-sectional area method.

A(x)dx | = | (4x^{2} - 40x + 100)dx | |

= | -20x^{2} + 100x | ||

= |

Take a Study Break!