Exercises: Volume of prisms, cylinders, pyramids, cones, spheres - ACT Math

A

Recall / Warm-Up

1.

What is the area of a rectangle with length 12 cm and width 5 cm?

A.

17 cm²

B.

34 cm²

C.

60 cm²

D.

120 cm²

2.

What is the area of a circle with radius 3 cm? Leave your answer in terms of $\pi$ .

A.

$6\pi$ cm²

B.

$9\pi$ cm²

C.

$12\pi$ cm²

D.

$27\pi$ cm²

3.

Which formula gives the area of a triangle?

A.

$A = bh$

B.

$A = \frac{1}{2}bh$

C.

$A = \pi r^2$

D.

$A = 2b + 2h$

B

Fluency Practice

C

Varied Practice

D

Word Problems / Application

1.

A grain silo is shaped like a cylinder topped with a cone. The cylinder has radius 5 m and height 12 m. The cone on top has the same radius and a height of 4 m.

What is the total volume of the silo? Express your answer in terms of $\pi$ .

2.

A basketball has a diameter of 24 cm. A tennis ball has a diameter of 6.5 cm.

1.

What is the volume of the basketball in terms of $\pi$ ?

2.

How many times larger is the basketball's volume than the tennis ball's volume? Round to the nearest whole number.

E

Error Analysis

1.

Sam solved this problem:

"A cone has radius 6 cm and height 15 cm. Find the volume."

Sam's work:

$B = \pi(6)^2 = 36\pi$
$V = 36\pi \times 15 = 540\pi$ cm³

What error did Sam make, and what is the correct volume?

A.

Sam forgot to multiply by $\frac{1}{3}$ . The correct volume is $180\pi$ cm³.

B.

Sam used the wrong base area. The correct volume is $270\pi$ cm³.

C.

Sam's answer of $540\pi$ cm³ is correct.

D.

Sam forgot to divide the base area by 2. The correct volume is $270\pi$ cm³.

2.

Jenna solved this problem:

"A sphere has diameter 10 cm. Find the volume."

Jenna's work:

$V = \frac{4}{3}\pi(10)^3$
$V = \frac{4}{3}\pi(1000)$
$V = \frac{4000\pi}{3}$ cm³

What error did Jenna make, and what is the correct volume?

A.

Jenna used the diameter instead of the radius. The correct volume is $\frac{500\pi}{3}$ cm³.

B.

Jenna should have used $\frac{4}{3}\pi r^2$ . The correct volume is $\frac{400\pi}{3}$ cm³.

C.

Jenna's answer of $\frac{4000\pi}{3}$ cm³ is correct.

D.

Jenna forgot to divide by 3. The correct volume is $\frac{4000\pi}{9}$ cm³.

F

Challenge / Extension

1.

A cone and a cylinder have the same radius and the same volume. If the cylinder has height 5 cm, what is the height of the cone in centimeters?

2.