Area and Volume Flashcards

A circular pool has radius 5 m. How much fencing (circumference) is needed? (Use π ≈ 3.14)

Answer: 31.4 m

C = 2πr = 2 × 3.14 × 5 = 31.4 m.

A right rectangular prism has length 8, width 5, and height 4. What is the total surface area?

Answer: 184

SA = 2(lw + lh + wh) = 2(40 + 32 + 20) = 2(92) = 184.

A sector has central angle 90° and radius 8 cm. What is its area in terms of π?

Answer: 16π cm²

Area = (90/360) × π(8²) = ¼ × 64π = 16π cm².

A ring is formed by a circle of radius 4 m minus a circle of radius 2 m at its center. What is the ring's area in terms of π?

Answer: 12π m²

Area = π(4²) − π(2²) = 16π − 4π = 12π m².

A triangular prism has a cross-section with base 5 cm and height 6 cm, and is 12 cm long. What is its volume?

Answer: 180 cm³

V = (½ × 5 × 6) × 12 = 15 × 12 = 180 cm³.

A circle's area equals the area of a square with side 10 cm. What is the approximate radius? (Use π ≈ 3.14)

Answer: 5.64 cm

πr² = 100 → r² = 100/3.14 ≈ 31.85 → r ≈ 5.64 cm.

A box has volume 360 cm³. If length and width are each doubled while height stays the same, what is the new volume?

Answer: 1,440 cm³

New V = (2l)(2w)(h) = 4lwh = 4 × 360 = 1,440 cm³.