Area and Volume Flashcards

A cone and a cylinder share the same radius and height. What is the ratio of the cone's volume to the cylinder's volume?

Answer: 1:3

Vcone = ⅓πr²h and Vcylinder = πr²h, so the ratio is ⅓:1 = 1:3.

A parallelogram has base 11 m and height 6 m. What is its area?

Answer: 66 m²

Area = base × height = 11 × 6 = 66 m².

A rectangular pool is 25 m × 10 m × 2 m deep. How many liters of water does it hold? (1 m³ = 1,000 L)

Answer: 500,000 L

Volume = 25 × 10 × 2 = 500 m³; 500 × 1,000 = 500,000 L.

A circular garden has radius 7 m. What is the area? (Use π ≈ 22/7)

Answer: 154 m²

A = πr² = (22/7) × 49 = 22 × 7 = 154 m².

The surface area of a cube is 150 cm². What is the side length?

Answer: 5 cm

6s² = 150 → s² = 25 → s = 5 cm.

A 10 cm × 6 cm rectangle has a right triangle with legs 6 cm and 4 cm removed from one corner. What is the remaining area?

Answer: 48 cm²

Rectangle = 60 cm²; triangle = ½ × 6 × 4 = 12 cm²; remaining = 60 − 12 = 48 cm².

A cylinder's radius is doubled while its height stays the same. By what factor does its volume increase?

Answer: 4

V = πr²h; doubling r → π(2r)²h = 4πr²h; volume increases by a factor of 4.