Area and Volume Flashcards

A triangle has vertices at (0, 0), (8, 0), and (3, 5). What is its area?

Answer: 20

Base = 8 (along x-axis), height = 5 (y-coordinate of apex); A = ½(8)(5) = 20.

A solid cylinder of radius 5 cm and height 12 cm has a cylindrical hole of radius 2 cm drilled all the way through the center. What is the remaining volume in terms of π?

Answer: 252π cm³

Full volume = π(25)(12) = 300π; hole volume = π(4)(12) = 48π; remaining = 252π cm³.

Two similar triangles have areas 9 cm² and 25 cm². What is the ratio of their corresponding side lengths?

Answer: 3:5

Area ratio = 9:25; side ratio = √9:√25 = 3:5.

An annulus (ring) has outer radius 10 cm and inner radius 6 cm. What is its area in terms of π?

Answer: 64π cm²

A = π(R² − r²) = π(100 − 36) = 64π cm².

A cone has the same base radius and height as a cylinder. The cylinder's volume is 60π. What is the cone's volume in terms of π?

Answer: 20π

Cone volume = (1/3) × cylinder volume = 60π/3 = 20π.

A circular pizza has a diameter of 14 inches. It is cut into 8 equal slices. What is the area of one slice? (Use π ≈ 22/7)

Answer: 19.25 in²

Total area = (22/7)(7²) = 154 in²; one slice = 154/8 = 19.25 in².

A rectangular prism has a volume of 504 cm³. Its length is 9 cm and width is 7 cm. What is its height?

Answer: 8 cm

V = lwh → 504 = 9 × 7 × h = 63h → h = 8 cm.