Area and Volume Flashcards

A cylindrical can has diameter 10 cm and height 15 cm. What is the volume? (Leave in terms of π)

Answer: 375π cm³

Radius = 5; V = π(5²)(15) = 375π cm³.

A trapezoid has area 90 cm², height 9 cm, and one parallel side 8 cm. What is the other parallel side?

Answer: 12 cm

90 = ½(8 + b₂)(9) → 20 = 8 + b₂ → b₂ = 12 cm.

A composite figure is a 10 m × 10 m square with a triangle of base 10 m and height 6 m on top. What is the total area?

Answer: 130 m²

Square = 100 m²; triangle = ½ × 10 × 6 = 30 m²; total = 130 m².

A hemisphere (half-sphere) has radius 6 cm. What is its volume in terms of π?

Answer: 144π cm³

Full sphere = (4/3)π(6³) = (4/3)π(216) = 288π; hemisphere = 144π cm³.

If the radius of a circle is increased by 50%, by what percent does the area increase?

Answer: 125%

New area = π(1.5r)² = 2.25πr²; percent increase = (2.25 − 1) × 100% = 125%.

A rectangular sandbox is 2 m × 3 m, filled with sand to a depth of 0.5 m. What is the volume of sand?

Answer: 3 m³

V = 2 × 3 × 0.5 = 3 m³.

A triangle has base 18 cm and area 108 cm². What is the height?

Answer: 12 cm

108 = ½ × 18 × h → h = 216/18 = 12 cm.