Question

The radius of a cylinder is 4 inches and the height is 5 inches. Which statements are correct? Check all that apply.

The area of the two bases is 16π in2.

The area of the two bases is 32π in2.

The lateral area is 40π in2.

The lateral area is 72π in2.

The total surface area is 72π in2.

The Correct Answer is: 2,3,5

Answer 1

The area of the two bases is 32π in2.

The lateral area is 40π in2.

The total surface area is 72π in2.

Explanation:

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Answer 2

- The area of the two bases is 32π in².

- The lateral area is 40π in².

- The total surface area is 72π in².

Explanation:

1. The base of the cylinder is a circle, therefore, you can apply the formula for calculate the area of a circle:

`A=r^(2)\pi`

Where
`r` is the radius.

Then the area of the base is:

`A_b=(4in)^(2)\pi=16in^(2)`

Multiply by 2 to obtain the area of the two bases:

`A_(bases)=2(16\pi)=32\pi`
`in^(2)`

2. The lateral area is (Where
`h` is the height):

`LA=2rh\pi=2(4in)(5in)\pi=40\pi`
`in^(2)`

3. The total surface area is calculated with the formula:

`A_t=2r^(2)\pi+h(2r\pi)`

Where
`h` is the height.

Then:

`A_t=2\pi(4in)^(2)+\pi(5in)(2)(4in)=72\pi`
`in^(2)`