Bluebook SAT Test Area and Volume 13

Question 1

A pentagon-shaped region is made of a 10 × 8 rectangle with an isosceles triangle (base 10, height 3) on top. What is the total area?

Accepted Answer

95

Answer

Rectangle area = 80; triangle area = (1/2)(10)(3) = 15; total = 95.

Question 2

The volume of a cube is 512 cm³. What is the total surface area of the cube?

Accepted Answer

384 cm²

Answer

Side = ∛512 = 8 cm; surface area = 6 × 8² = 6 × 64 = 384 cm².

Question 3

A farmer's circular field has diameter 56 m. What is the area of the field? (Use π ≈ 22/7)

Accepted Answer

2464 m²

Answer

Radius = 28 m; A = (22/7)(28²) = (22/7)(784) = 2464 m².

Question 4

A solid metal ball of radius 3 cm is melted and recast into a cylinder of radius 3 cm. What is the height of the cylinder? (Leave in terms of π if needed.)

Accepted Answer

4 cm

Answer

Sphere volume = (4/3)π(27) = 36π; cylinder volume = π(9)h = 36π → h = 4 cm.

Question 5

A rectangular carpet 6 m × 4 m costs $18 per square meter. How much does the carpet cost?

Accepted Answer

$432

Answer

Area = 24 m²; cost = 24 × 18 = $432.

Bluebook SAT Practice Test

Bluebook SAT Practice Test

Bluebook SAT Test Area and Volume 13