Answer: The volume of the cylinder is 640π cm³
Explanation:
The formula of the surface area of a cylinder is SA = 2πrh + 2πr², where r is the radius of its base and h is its height
The formula of the volume of a cylinder is V = πr²h
Let us use the formula of the surface area to find the height of the cylinder, then use the formula of the volume to find its volume
∵ The surface area of a cylinder is 288π cm²
∵ Its radius is 8 cm
∵ SA = 2πrh + 2πr²
- Substitute the SA by 288π and r by 8 in the formula
∴ 288π = 2π(8)h + 2π(8)²
∴ 288π = 16πh + 128π
- Subtract 128π from both sides
∴ 160π = 16πh
- Divide both sides by 16π
∴ 10 = h
∴ The height of the cylinder is 10 cm
Now let us find the volume of the cylinder
∵ V = πr²h
- Substitute r by 8 and h by 10
∴ V = π(8)²(10)
∴ V = π(64)(10)
∴ V = 640π
The volume of the cylinder is 640π cm³