Geometric Area and Volume Flashcards

A circular pizza has a diameter of 16 inches. What is the area of the entire pizza? (Use π ≈ 3.14)

Answer: 200.96 square inches

Radius = 8 inches; Area = π × r² = 3.14 × 64 = 200.96 square inches.

A storage unit is shaped like a rectangular prism with dimensions 8 ft × 6 ft × 5 ft. What is its volume?

Answer: 240 cubic feet

Volume = length × width × height = 8 × 6 × 5 = 240 cubic feet.

If you double the radius of a circle, the area becomes how many times larger?

Answer: 4 times larger

Area = πr²; doubling r gives π(2r)² = 4πr², so the area is 4 times larger.

A semicircle has a diameter of 20 cm. What is the area of the semicircle? (Use π ≈ 3.14)

Answer: 157 square cm

Radius = 10 cm; Semicircle area = ½ × π × r² = ½ × 3.14 × 100 = 157 square cm.

A rectangular garden plot is 18 feet long. If its area is 216 square feet, what is its width?

Answer: 12 feet

Width = Area ÷ Length = 216 ÷ 18 = 12 feet.

A triangular prism has a triangular face with base 6 cm and height 4 cm, and a length of 10 cm. What is its volume?

Answer: 120 cubic cm

Volume = area of triangle × length = (½ × 6 × 4) × 10 = 12 × 10 = 120 cubic cm.

Which shape has the largest area: a square with side 6 cm, a circle with radius 3.5 cm, or a rectangle 8 cm × 4 cm? (Use π ≈ 3.14)

Answer: Circle (38.47 sq cm)

Square = 36 sq cm; Circle = 3.14 × 3.5² = 38.465 sq cm; Rectangle = 32 sq cm — the circle is largest.