Area and Volume Flashcards

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

Answer: 7 cm

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

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

Answer: 65π cm²

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

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

Answer: 6

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

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

Answer: 60 cm²

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

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)

Answer: 157 min

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

The ratio of the radii of two spheres is 1:2. What is the ratio of their surface areas?

Answer: 1:4

Surface area = 4πr²; ratio = r₁²:r₂² = 1²:2² = 1:4.

A right circular cone is cut parallel to its base at the midpoint of its height, creating a smaller top cone. What fraction of the original volume is the smaller cone?

Answer: 1/8

The top cone has half the height and half the radius (similar shapes), so its volume = (1/2)³ = 1/8 of the original.