Area and Volume Flashcards

A pentagon-shaped region is made of a 10 × 8 rectangle with an isosceles triangle (base 10, height 3) on top. What is the total area?

Answer: 95

Rectangle area = 80; triangle area = (1/2)(10)(3) = 15; total = 95.

The volume of a cube is 512 cm³. What is the total surface area of the cube?

Answer: 384 cm²

Side = ∛512 = 8 cm; surface area = 6 × 8² = 6 × 64 = 384 cm².

A farmer's circular field has diameter 56 m. What is the area of the field? (Use π ≈ 22/7)

Answer: 2464 m²

Radius = 28 m; A = (22/7)(28²) = (22/7)(784) = 2464 m².

A solid metal ball of radius 3 cm is melted and recast into a cylinder of radius 3 cm. What is the height of the cylinder? (Leave in terms of π if needed.)

Answer: 4 cm

Sphere volume = (4/3)π(27) = 36π; cylinder volume = π(9)h = 36π → h = 4 cm.

A rectangular carpet 6 m × 4 m costs $18 per square meter. How much does the carpet cost?

Answer: $432

Area = 24 m²; cost = 24 × 18 = $432.

A prism has a trapezoidal cross-section with parallel sides 5 cm and 9 cm and height 4 cm. The prism is 10 cm long. What is its volume?

Answer: 280 cm³

Trapezoid area = ½(5+9)(4) = ½(14)(4) = 28; volume = 28 × 10 = 280 cm³.

When the radius of a circle is increased by 20%, by what percent does the area increase?

Answer: 44%

New radius = 1.2r; new area = π(1.2r)² = 1.44πr²; increase = 44%.