Bluebook SAT Test Area and Volume 3

Question 1

What is the area of a circle with diameter 10? (Leave answer in terms of π)

Accepted Answer

25π

Answer

Radius = 5; Area = π(5²) = 25π.

Question 2

A rectangular prism has volume 180 cm³, length 9 cm, and width 4 cm. What is its height?

Accepted Answer

5 cm

Answer

h = V ÷ (l × w) = 180 ÷ 36 = 5 cm.

Question 3

The length of a rectangle is twice its width. If the area is 72 m², what is the width?

Accepted Answer

6 m

Answer

Let w = width, l = 2w; A = 2w² = 72 → w² = 36 → w = 6 m.

Question 4

A trapezoid has parallel sides of 8 cm and 12 cm, and a height of 5 cm. What is its area?

Accepted Answer

50 cm²

Answer

A = ½(b₁ + b₂)h = ½(8 + 12)(5) = ½ × 20 × 5 = 50 cm².

Question 5

A sphere's radius is tripled. By what factor does its volume increase?

Accepted Answer

27

Answer

Volume ∝ r³; tripling r multiplies volume by 3³ = 27.

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