Bluebook SAT Test Area and Volume 16

Question 1

A sphere has surface area 196π cm². What is its diameter?

Accepted Answer

14 cm

Answer

SA = 4πr² = 196π → r² = 49 → r = 7; diameter = 14 cm.

Question 2

A composite solid consists of a cube with side 6 cm and a square pyramid (same base, height 4 cm) on top. What is the total volume?

Accepted Answer

264 cm³

Answer

Cube = 6³ = 216; pyramid = (1/3)(36)(4) = 48; total = 264 cm³.

Question 3

The perimeter of a rectangle is 48 cm and its length is 14 cm. What is the area of the rectangle?

Accepted Answer

140 cm²

Answer

2(l + w) = 48 → l + w = 24 → w = 10; area = 14 × 10 = 140 cm².

Question 4

A cylindrical pipe has outer diameter 10 cm, inner diameter 8 cm, and length 50 cm. What is the volume of the metal (hollow section) in terms of π?

Accepted Answer

450π cm³

Answer

Outer radius = 5, inner radius = 4; volume = π(25 − 16)(50) = π(9)(50) = 450π cm³.

Question 5

A triangle has base 20 m and height 9 m. If both the base and height are reduced by 40%, what is the new area?

Accepted Answer

32.4 m²

Answer

New base = 12, new height = 5.4; new area = ½(12)(5.4) = 32.4 m².

Bluebook SAT Practice Test