Question

45 points please help ASAP part 3

What is the volume of a cylinder with a height of 8 in. and a diameter of 6 in.? Provide the exact answer.

Answer 1

72
`\pi` inches^3

Explanation:

The formula for the volume of a cylinder is V =
`\pi r^2h`, where r represents the radius of the cylinder (radius is the length of half the diameter) and h represents the height of the cylinder).

The question gives the diameter of the cylinder, so to find the radius the diameter would have to be divided by 2.

• 6 / 2 = 3

The radius of the cylinder is 3 inches. The height of the cylinder is already given, so we can proceed in finding the volume of the cylinder using the formula V =
`\pi r^2h`.

Substitute 3 for r and 8 for h.

• V =
  `\pi (3)^2(8)`

Start by evaluating the exponent.

• V =
  `\pi (9)(8)`

Multiply 9 and 8 together.

• V =
  `\pi (72)`

The question is looking for the exact answer, therefore the answer would just end here. The final and most exact answer is 72
`\pi` inches^3 (which is 226.194671 inches^3 or if rounded, 226.19 inches^3).

Answer 2

V = 72π in ^3

Explanation:

The volume of a cylinder is given by the formula

V =pi r^2 h

We know the height is 8 and the diameter is 6

We need to find the radius

d= 2r

6= 2r

6/2 = 2r/2

3 =r

We can substitute in. We must keep pi as pi to be exact,

V = pi * 3^2 *8

V = pi * 9*8

V =72 pi

V = 72π in ^3