Bluebook SAT Test Area and Volume 12

Question 1

A parallelogram has area 84 cm² and base 12 cm. What is its height?

Accepted Answer

7 cm

Answer

A = base × height → 84 = 12h → h = 7 cm.

Question 2

A cone has slant height 13 cm and radius 5 cm. What is the lateral surface area in terms of π?

Accepted Answer

65π cm²

Answer

Lateral SA = πrl = π(5)(13) = 65π cm².

Question 3

A rectangle's length is 3 more than twice its width. If the area is 54, what is the width?

Accepted Answer

6

Answer

Let width = w; length = 2w − 3; w(2w − 3) = 54 → 2w² − 3w − 54 = 0 → (2w + 9)(w − 6) = 0 → w = 6.

Question 4

A kite has diagonals of 15 cm and 8 cm. What is its area?

Accepted Answer

60 cm²

Answer

Area = (d₁ × d₂)/2 = (15 × 8)/2 = 60 cm².

Question 5

A cylindrical tank has radius 5 m and height 4 m. Water is pumped in at 2 m³/min. How many minutes to fill it? (Use π ≈ 3.14)

Accepted Answer

157 min

Answer

Volume = π(25)(4) = 100π ≈ 314 m³; time = 314/2 = 157 min.

Bluebook SAT Practice Test