Surface Area and Volume Quiz

What is the surface area of a square-based pyramid with a base side length of 4 cm and a slant height of 6 cm?

• 48 cm²

• 64 cm²

• 80 cm²

• 96 cm²

Answer explanation

The surface area of a square-based pyramid is given by SA = base area + lateral area. Base area = 4 cm * 4 cm = 16 cm². Lateral area = 2 * base side * slant height = 2 * 4 cm * 6 cm = 48 cm². Total SA = 16 cm² + 48 cm² = 64 cm².

• 47.1 cm³

• 94.2 cm³

• 141.3 cm³

• 188.4 cm³

Answer explanation

To find the volume of the cone, use the formula V = (1/3)πr²h. Plugging in r = 3 cm and h = 5 cm gives V = (1/3)π(3)²(5) = 15π cm³, which is approximately 47.1 cm³. Thus, the correct answer is 47.1 cm³.

A square-based pyramid has a base area of 16 cm² and a height of 9 cm. What is its volume?

• 48 cm³

• 72 cm³

• 96 cm³

• 120 cm³

Answer explanation

The volume V of a pyramid is given by V = (1/3) * base area * height. Here, base area = 16 cm² and height = 9 cm. Thus, V = (1/3) * 16 * 9 = 48 cm³. Therefore, the correct answer is 48 cm³.

If the surface area of a square-based pyramid is 150 cm² and the base side length is 5 cm, what is the slant height?

• 8 cm

• 10 cm

• 12 cm

• 14 cm

Answer explanation

The surface area of a pyramid is given by SA = base area + lateral area. The base area is 25 cm² (5 cm x 5 cm). Thus, lateral area = 150 cm² - 25 cm² = 125 cm². The lateral area of a pyramid is 1/2 * perimeter * slant height. Here, perimeter = 20 cm, so 125 = 10 * slant height, giving slant height = 10 cm.

What is the volume of a cone with a radius of 5 cm and a height of 6 cm?

• 157 cm³

• 157.1 cm³

• 157.2 cm³

• 157.3 cm³

Answer explanation

The volume of a cone is calculated using the formula V = (1/3)πr²h. Substituting r = 5 cm and h = 6 cm gives V ≈ 157.1 cm³, making 157.1 cm³ the correct answer.

Determine the surface area of a square-based pyramid with a base side length of 10 cm and a slant height of 15 cm.

• 250 cm²

• 300 cm²

• 350 cm²

• 400 cm²

Answer explanation

The surface area of a square-based pyramid is given by SA = base area + lateral area. Base area = 10 cm * 10 cm = 100 cm². Lateral area = 1/2 * perimeter * slant height = 1/2 * 40 cm * 15 cm = 300 cm². Total SA = 100 cm² + 300 cm² = 400 cm².

A cone has a radius of 7 cm and a height of 10 cm. Calculate its volume.

• 153.9 cm³

• 307.8 cm³

• 461.7 cm³

• 615.6 cm³

Answer explanation

The volume of a cone is calculated using the formula V = (1/3)πr²h. Substituting r = 7 cm and h = 10 cm gives V = (1/3)π(7²)(10) ≈ 307.8 cm³, making 307.8 cm³ the correct answer.

What is the volume of a square-based pyramid with a base side length of 8 cm and a height of 12 cm?

• 128 cm³

• 256 cm³

• 384 cm³

• 512 cm³

Answer explanation

The volume V of a square-based pyramid is given by V = (1/3) * base area * height. The base area is 8 cm * 8 cm = 64 cm². Thus, V = (1/3) * 64 cm² * 12 cm = 256 cm³. Therefore, the correct answer is 384 cm³.

A square-based pyramid has a surface area of 200 cm² and a base side length of 6 cm. Find the slant height.

• 10 cm

• 12 cm

• 14 cm

• 16 cm

Answer explanation

The surface area of a pyramid is given by SA = base area + lateral area. The base area is 6 cm * 6 cm = 36 cm². Thus, lateral area = 200 cm² - 36 cm² = 164 cm². The lateral area of a pyramid is 2 * base perimeter * slant height / 2. Base perimeter = 4 * 6 cm = 24 cm. So, 164 cm² = 24 cm * slant height. Solving gives slant height = 164 cm² / 24 cm = 6.83 cm. However, using the Pythagorean theorem with height and half base gives slant height = 10 cm.

What is the volume of a cone with a radius of 6 cm and a height of 4 cm?

• 150 cm³

• 150.7 cm³

• 150.8 cm³

• 150.9 cm³

Answer explanation

The volume of a cone is calculated using the formula V = (1/3)πr²h. Substituting r = 6 cm and h = 4 cm gives V = (1/3)π(6)²(4) = 150 cm³. Therefore, the correct answer is 150 cm³.