Mathematics: Geometry and Measurement Flashcards

What is the area of a circle with a diameter of 10 meters? (Use π ≈ 3.14)

Answer: 78.5 m²

Radius = 5 m; Area = πr² = 3.14 × 25 = 78.5 m².

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

Answer: 150.72 cm³

Volume = (1/3)πr²h = (1/3)(3.14)(16)(9) = 150.72 cm³.

How many feet are in 3 miles?

Answer: 15,840 ft

1 mile = 5,280 feet, so 3 miles = 3 × 5,280 = 15,840 feet.

A rectangular garden is 15 m long and 8 m wide. A path 1 m wide runs along the inside edge all around. What is the area of the path?

Answer: 42 m²

Outer area = 15 × 8 = 120 m²; inner area = 13 × 6 = 78 m²; path area = 120 − 78 = 42 m².

What is the measure of each interior angle of a regular pentagon?

Answer: 108°

Sum of interior angles = (5−2) × 180° = 540°; each angle = 540°/5 = 108°.

A rectangle has an area of 84 cm² and a length of 12 cm. What is its perimeter?

Answer: 38 cm

Width = 84/12 = 7 cm; Perimeter = 2(12 + 7) = 2(19) = 38 cm.

Two complementary angles differ by 18°. What is the measure of the smaller angle?

Answer: 36°

Let angles be x and x + 18; x + x + 18 = 90°, so 2x = 72°, x = 36°.