Answer:
The volume of the cylinder is 108 π units³
Explanation:
- The formula of the volume of the cone is V =
πr²h, where r is the radius of its base and h is its height - The formula of the volume of a cylinder is V = πr²h, where r is the radius of its base and h is its height
∵ The area of the base of the cylinder is equal to the area of
the base of the cone
∴ Their radii are equal
∵ The height of the cylinder is equal to the height of the cone
∵ The volume of the cone = 36 π units³
- Equate the formula of the volume of the cone by 36 π
∵ 36 π =
πr²h
- Multiply both sides by 3
∴ 108 π = πr²h
- Divide both sides by π
∴ 108 = r²h
- Substitute the value of r²h in the formula of the volume of
the cylinder
∵ V = πr²h
∴ V = π (108) = 108 π
∴ The volume of the cylinder is 108 π units³