Free Printable Unit 9 Practice Test

1.

If you were to find the volume of the solid created by revolving the region bounded by

y=2x^4-2x

and

y=\sin x

about the line y = -2, which method should you use?

a)

Disk

b)

Washer

c)

Shell

d)

Washer or Shell

2.

What is the volume of this solid of revolution?

a)

$\pi\int_2^8\ \left(x-2\right)^2dx$

b)

$\pi\int_2^8\ \left(x+2\right)^2dx$

c)

$\int_2^8\ \left(x-2\right)^2dx$

d)

$\pi\int_2^8\ \left(x+2\right)^{ }dx$

3.

Find the volume of the solid of revolution obtained by rotating the region in bounded by y = x³ + 1, x = 1 and y = 1 about the y-axis.

a)

11π/3

b)

4π/13

c)

3π/7

d)

2π/5

4.

If the region enclosed by y = x² + 4 and y = 2x + 4 is revolved about the x-axis, what is the volume of the solid generated?

a)

224π/15

b)

8π

c)

416π/15

d)

16π/5

5.

a)

b)

c)

d)

6.

a)

A

b)

B

c)

C

d)

D

7.

a)

A

b)

B

c)

C

d)

D

8.

Write the integral that can be used to find the region bounded by x = -3y² + 4 and x = y³.

a)

b)

c)

d)

e)

9.

The base of a solid is the region in the first quadrant enclosed by the graph of 𝑦 = 2 − 𝑥² and the coordinate axes. If every cross section of the solid perpendicular to the 𝑦-axis is a square, the volume of the solid is given by...

a)

$\int_0^2\left(2-x^2\right)^2dx$

b)

$\int_0^2\sqrt{2-y}dy$

c)

$\int_0^2\left(2-y\right)dy$

d)

$\int_0^2\left(2-x^2\right)dx$

10.

The base of a solid is the region in the first quadrant enclosed by the parabola 𝑦 = 4𝑥² , the line 𝑥 = 1, and the 𝑥-axis. Each plane section of the solid perpendicular to the 𝑥-axis is a square. The volume of the solid is…

a)

4/3

b)

16/5

c)

4

d)

16

Unit 9 Practice Test

Total questions: 10

Worksheet time: 50mins

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