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4 years ago

If the surface area of a cylinder is 288π cm2 with radius of 8 cm, what is the volume of the cylinder?

Mathematics

1 answer:

Furkat [3]4 years ago

7 0

Answer:

The volume of the cylinder is 640π cm³

Step-by-step 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

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If the surface area of a cylinder is 288π cm2 with radius of 8 cm, what is the volume of the cylinder?​

If the surface area of a cylinder is 288π cm2 with radius of 8 cm, what is the volume of the cylinder?