Area and Volume Flashcards

A sphere has surface area 196π cm². What is its diameter?

Answer: 14 cm

SA = 4πr² = 196π → r² = 49 → r = 7; diameter = 14 cm.

A composite solid consists of a cube with side 6 cm and a square pyramid (same base, height 4 cm) on top. What is the total volume?

Answer: 264 cm³

Cube = 6³ = 216; pyramid = (1/3)(36)(4) = 48; total = 264 cm³.

The perimeter of a rectangle is 48 cm and its length is 14 cm. What is the area of the rectangle?

Answer: 140 cm²

2(l + w) = 48 → l + w = 24 → w = 10; area = 14 × 10 = 140 cm².

A cylindrical pipe has outer diameter 10 cm, inner diameter 8 cm, and length 50 cm. What is the volume of the metal (hollow section) in terms of π?

Answer: 450π cm³

Outer radius = 5, inner radius = 4; volume = π(25 − 16)(50) = π(9)(50) = 450π cm³.

A triangle has base 20 m and height 9 m. If both the base and height are reduced by 40%, what is the new area?

Answer: 32.4 m²

New base = 12, new height = 5.4; new area = ½(12)(5.4) = 32.4 m².

A square has the same area as a circle with radius 6. What is the approximate side length of the square? (Use π ≈ 3.14)

Answer: 10.63

Circle area = 3.14 × 36 = 113.04; side = √113.04 ≈ 10.63.

A water tank shaped like a rectangular prism holds 3,000 liters. Its base is 2 m × 1.5 m. How tall is the tank? (1 m³ = 1,000 L)

Answer: 1 m

Volume = 3 m³; h = 3 / (2 × 1.5) = 3/3 = 1 m.