Question

A cylindrical soap dispenser has a diameter of 3 inches and a height of 10 inches. 3 in. 10 in. Which measurement is closest to the total surface area of the dispenser in square inches? F 203 in. 2 G 108 in.2 H 245 in.2 122 in.2

Answer 1

start by calculating the are of the top and bottom of the cylinder using the formula

`A=\pi\cdot r^2`
`\begin{gathered} A=\pi\cdot(1.5)^2 \\ A\approx7.07 \end{gathered}`

Now calculate the side surface area using the arc length of the base and the height of the cylinder

`A=2\cdot\pi\cdot r\cdot h`
`\begin{gathered} A=2\cdot\pi\cdot1.5\cdot10 \\ A=30\pi \\ A\approx94.28 \end{gathered}`

calculate the total area by adding the top, bottom and sides areas

`\begin{gathered} A=94.28+7.07+7.07 \\ A\approx108.42 \end{gathered}`