Question

Find the volume of each cylinder in terms of π. Which cylinder has the greater volume?

Cylinder A: Area of base = 6π ft², height = 10 ft.
Cylinder B: Circumference = 6π ft, height = 6 ft.
A. The volume of Cylinder A is greater.
B. The volume of Cylinder B is greater.
C. The volumes of both cylinders are equal.
D. The volume cannot be determined with the given information.

Answer 1

The volume of Cylinder A is greater than the volume of Cylinder B. Hence the correct answer is option A

Step-by-step explanation:

To find the volume of each cylinder, we can use the formula V = πr²h, where V is the volume, r is the radius of the base, and h is the height. For Cylinder A, the area of the base is given as 6π ft², so the radius is sqrt(6π/π) = sqrt(6) ft. The height is 10 ft. Plugging these values into the formula, we get V = π(sqrt(6) ft)² * 10 ft = 60π ft³. For Cylinder B, the circumference is given as 6π ft, so the radius is (6π ft) / (2π) = 3 ft. The height is 6 ft. Plugging these values into the formula, we get V = π(3 ft)² * 6 ft = 54π ft³.

Therefore, the volume of Cylinder A is 60π ft³ and the volume of Cylinder B is 54π ft³. Since 60π is greater than 54π, the volume of Cylinder A is greater.

Hence the correct answer is option A