Mathematics: Geometry and Measurement Flashcards

A cylindrical water tank has a radius of 3 feet and a height of 10 feet. What is its volume in cubic feet?

Answer: 90π

Volume of a cylinder = πr²h = π(3²)(10) = 90π cubic feet.

Two angles of a triangle measure 47° and 83°. What is the measure of the third angle?

Answer: 50°

The sum of angles in a triangle is 180°, so the third angle = 180° − 47° − 83° = 50°.

A rectangle has a perimeter of 56 cm and a width of 10 cm. What is its length?

Answer: 18 cm

Perimeter = 2(l + w), so 56 = 2(l + 10), giving l = 18 cm.

What is the area of a trapezoid with bases of 8 cm and 14 cm and a height of 5 cm?

Answer: 55 cm²

Area = ½(b₁ + b₂)h = ½(8 + 14)(5) = ½(22)(5) = 55 cm².

A diagonal of a square is 10 inches. What is the area of the square?

Answer: 50 in²

Area of a square from diagonal d = d²/2 = 100/2 = 50 in².

How many cubic inches are in 2 cubic feet?

Answer: 3,456 in³

1 cubic foot = 12³ = 1,728 cubic inches, so 2 cubic feet = 3,456 cubic inches.

A circle has a circumference of 31.4 cm. What is its radius? (Use π ≈ 3.14)

Answer: 5 cm

C = 2πr, so r = C/(2π) = 31.4/(2 × 3.14) = 5 cm.