Geometric Area and Volume Flashcards

A room floor measures 15 feet by 12 feet. Carpet costs $3.50 per square foot. How much will it cost to carpet the entire floor?

Answer: $630

Area = 15 × 12 = 180 sq ft; Cost = 180 × $3.50 = $630.

A cylindrical can has a diameter of 10 cm and a height of 15 cm. What is the lateral (side) surface area? (Use π ≈ 3.14)

Answer: 471 square cm

Lateral SA = 2πrh = 2 × 3.14 × 5 × 15 = 471 square cm.

Two identical triangles are cut from a rectangle measuring 10 cm × 6 cm. What area remains?

Answer: 30 square cm

Rectangle area = 60 sq cm; two triangles that together equal the rectangle = 60 sq cm; remaining = 60 - 30 = 30 sq cm (one triangle's area).

A pyramid has a square base with sides of 6 m and a height of 8 m. What is its volume?

Answer: 96 cubic meters

Volume of a pyramid = (1/3) × base area × height = (1/3) × 36 × 8 = 96 cubic meters.

A parallelogram has a base of 14 cm and a height of 7 cm. What is its area?

Answer: 98 square cm

Area of a parallelogram = base × height = 14 × 7 = 98 square cm.

A hollow pipe has an outer radius of 5 cm and an inner radius of 3 cm. What is the area of its circular cross-section? (Use π ≈ 3.14)

Answer: 50.24 square cm

Area = π(R² - r²) = 3.14 × (25 - 9) = 3.14 × 16 = 50.24 square cm.

A box without a lid is 8 inches long, 5 inches wide, and 4 inches tall. What is the total surface area of the box (5 sides only)?

Answer: 144 square inches

Bottom = 8×5 = 40; two long sides = 2(8×4) = 64; two short sides = 2(5×4) = 40; Total = 40 + 64 + 40 = 144 square inches.