Bluebook SAT Test Area and Volume 10

Question 1

An equilateral triangle has side length 8. What is its area? (Leave answer in simplified radical form.)

Accepted Answer

16√3

Answer

Area = (√3/4)s² = (√3/4)(64) = 16√3.

Question 2

A cylinder has radius 3 and height h. If the volume is 54π, what is h?

Accepted Answer

6

Answer

V = πr²h → 54π = π(9)h → h = 54/9 = 6.

Question 3

A trapezoid has parallel sides of 7 ft and 13 ft. If its area is 100 ft², what is its height?

Accepted Answer

10 ft

Answer

A = ½(b₁ + b₂)h → 100 = ½(20)h = 10h → h = 10.

Question 4

A rectangular prism has surface area 94 cm². Its length is 5 cm and width is 4 cm. What is its height?

Accepted Answer

3 cm

Answer

SA = 2(lw + lh + wh) → 94 = 2(20 + 5h + 4h) → 47 = 20 + 9h → h = 3.

Question 5

A sector of a circle has radius 10 and central angle 72°. What is its arc length? (Leave in terms of π.)

Accepted Answer

4π

Answer

Arc length = (72/360)(2π)(10) = (1/5)(20π) = 4π.

Bluebook SAT Practice Test