BMST Geometric Area and Volume 4

Question 1

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?

Accepted Answer

$630

Answer

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

Question 2

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)

Accepted Answer

471 square cm

Answer

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

Question 3

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

Accepted Answer

30 square cm

Answer

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).

Question 4

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

Accepted Answer

96 cubic meters

Answer

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

Question 5

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

Accepted Answer

98 square cm

Answer

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

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