Bluebook SAT Test Area and Volume 9

Question 1

A rhombus has diagonals of length 10 cm and 16 cm. What is the area of the rhombus?

Accepted Answer

80 cm²

Answer

Area of a rhombus = (d₁ × d₂) / 2 = (10 × 16) / 2 = 80 cm².

Question 2

A rectangular swimming pool measures 15 m × 8 m and is uniformly 2 m deep. How many cubic meters of water does it hold?

Accepted Answer

240 m³

Answer

Volume = length × width × depth = 15 × 8 × 2 = 240 m³.

Question 3

A circle is inscribed in a square with side length 6. What is the area of the region inside the square but outside the circle? (Use π ≈ 3.14)

Accepted Answer

7.74

Answer

Square area = 36; circle area = π(3)² ≈ 28.26; difference = 36 − 28.26 = 7.74.

Question 4

A triangular prism has a right-triangle base with legs 5 cm and 12 cm. The prism's length is 9 cm. What is the volume?

Accepted Answer

270 cm³

Answer

Base area = (1/2)(5)(12) = 30 cm²; volume = 30 × 9 = 270 cm³.

Question 5

A square piece of land has area 225 m². A path 1 m wide runs along the inside perimeter. What is the area of the path?

Accepted Answer

56 m²

Answer

Side = 15 m; inner square side = 13 m; inner area = 169 m²; path area = 225 − 169 = 56 m².

Bluebook SAT Practice Test