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## AP®︎ Calculus AB (2017 edition)

### Course: AP®︎ Calculus AB (2017 edition)>Unit 11

Lesson 6: Volume: disc method

# Disc method worksheet

Gain some risk-free experience with applying the disc method in this worksheet, before you attempt our exercise.

## Problem 1

A region is enclosed by the $x$-axis, the line $x=1$, the line $x=4$, and the curve $y=\sqrt{x}$.
What is the volume of the solid generated when this region is rotated around the $x$-axis?

## Problem 2

A region is enclosed by the $x$-axis and the curve $y={x}^{2}-2x$.
What is the volume of the solid generated when this region is rotated around the $x$-axis?

## Problem 3

A region is enclosed by the $y$-axis, the line $y=4$ and the curve $y=\frac{1}{2}{x}^{3}$.
What is the volume of the solid generated when this region is rotated around the line $y=4$?

## Problem 4

A region is enclosed by the positive $x$-axis, the positive $y$-axis and the curve $x=\sqrt{16-{y}^{2}}$ .
What is the volume of the solid generated when this region is rotated around the $y$-axis?

## Problem 5

A region is enclosed by the $y$-axis, the line $y=1$ and the curve $y={x}^{\frac{2}{3}}$.
What is the volume of the solid generated when this region is rotated around the $y$-axis?

## Problem 6

A region is enclosed by the $x$-axis, the line $x=9$, and the curve $y=\sqrt{x}$.
What is the volume of the solid generated when this region is rotated around the line $x=9$?

## Want to join the conversation?

• For problem 6, isn't the radius of the disc (9 - y), not (9 - y^2)? The explanation says you can "see this from the graph" but what I see is [9 - f(x)] and f(x) = Y; therefore, r = (9 - y), right?