1 Answer

Mindmatters · Answer 1 · 2023-12-23T08:28:52+0000

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

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