Question

The surface area of a cylinder is 325 in2 inches. Thelateral area is 200 in2.What is the radius of each of the bases?Round the answer to the nearest tenth.

Answer 1

The surface area of the cylinder = lateral area + 2 base area

Since the surface area = 325 in^2

Since the lateral area = 200 in^2

Subtract them to find 2 base area

2 base area = 325 - 200 = 125

Divide it by 2 to find the base area

`\begin{gathered} b\mathrm{}A=(125)/(2) \\ b\mathrm{}A=62.5 \end{gathered}`

Since the base of the cylinder is a circle

Since the area of the circle is

`b\mathrm{}A=\pi* r^2`

Substitute bA by 62.5

`62.5=\pi* r^2`

Divide both sides by pi

`(62.5)/(\pi)=r^2`

Take a square root for both sides

`\begin{gathered} \sqrt[]{(62.5)/(\pi)}=r \\ r=4.46031092 \end{gathered}`

Round it to the nearest tenth

r = 4.5 inches