Geometric Area and Volume Flashcards

A sphere has a radius of 6 cm. What is its volume? (Use π ≈ 3.14)

Answer: 904.32 cubic cm

Volume of a sphere = (4/3) × π × r³ = (4/3) × 3.14 × 216 = 904.32 cubic cm.

A farmer wants to fence a rectangular field 120 yards long and 85 yards wide. What is the total area of the field?

Answer: 10,200 square yards

Area = length × width = 120 × 85 = 10,200 square yards.

A cone has a base radius of 4 inches and a height of 9 inches. What is its volume? (Use π ≈ 3.14)

Answer: 150.72 cubic inches

Volume of a cone = (1/3) × π × r² × h = (1/3) × 3.14 × 16 × 9 = 150.72 cubic inches.

The base of a right triangle is 9 meters and the hypotenuse is 15 meters. What is the area of the triangle?

Answer: 54 square meters

Using the Pythagorean theorem, height = √(15² - 9²) = √144 = 12 m; Area = ½ × 9 × 12 = 54 square meters.

A square tile has a side of 9 inches. How many tiles are needed to cover a floor area of 3,645 square inches?

Answer: 45 tiles

Area of one tile = 9² = 81 square inches; Number of tiles = 3,645 ÷ 81 = 45 tiles.

A rectangular prism has a length of 10 m, width of 4 m, and height of 3 m. What is the total surface area?

Answer: 164 square meters

SA = 2(lw + lh + wh) = 2(40 + 30 + 12) = 2 × 82 = 164 square meters.

A circular fountain has a circumference of 31.4 feet. What is the area of its surface? (Use π ≈ 3.14)

Answer: 78.5 square feet

C = 2πr → r = 31.4 ÷ (2 × 3.14) = 5 ft; Area = π × 5² = 3.14 × 25 = 78.5 square feet.