Bluebook SAT Test Area and Volume 15

Question 1

A triangle has vertices at (0, 0), (8, 0), and (3, 5). What is its area?

Accepted Answer

20

Answer

Base = 8 (along x-axis), height = 5 (y-coordinate of apex); A = ½(8)(5) = 20.

Question 2

A solid cylinder of radius 5 cm and height 12 cm has a cylindrical hole of radius 2 cm drilled all the way through the center. What is the remaining volume in terms of π?

Accepted Answer

252π cm³

Answer

Full volume = π(25)(12) = 300π; hole volume = π(4)(12) = 48π; remaining = 252π cm³.

Question 3

Two similar triangles have areas 9 cm² and 25 cm². What is the ratio of their corresponding side lengths?

Accepted Answer

3:5

Answer

Area ratio = 9:25; side ratio = √9:√25 = 3:5.

Question 4

An annulus (ring) has outer radius 10 cm and inner radius 6 cm. What is its area in terms of π?

Accepted Answer

64π cm²

Answer

A = π(R² − r²) = π(100 − 36) = 64π cm².

Question 5

A cone has the same base radius and height as a cylinder. The cylinder's volume is 60π. What is the cone's volume in terms of π?

Accepted Answer

20π

Answer

Cone volume = (1/3) × cylinder volume = 60π/3 = 20π.

Bluebook SAT Practice Test

Bluebook SAT Practice Test

Bluebook SAT Test Area and Volume 15