Question

The otherSites Squared10.A cylinder has a diameter of 12 meters and a height of 9 meters. What is thetotal surface area of the cylinder? Give your answer to the nearest tenth, anduse 3.14 for pi

Answer 1

The total surface area of a cylinder is given by the formula

$\begin{gathered} A_{cylinder}=2circular\text{ area+curved surface area} \\ =2\pi r^2+2\pi rh \end{gathered}$

Given diameter, d=12meters, we will solve for radius

$\begin{gathered} \text{diameter,d}=2\times radius,r \\ d=2r \\ r=\frac{d}{2} \\ r=\frac{12m}{2} \\ r=6m \end{gathered}$

The height is given as 9meters

Substituting for r and h in the formula will give

$\begin{gathered} A_{cylinder}=2\pi r^2+2\pi rh \\ r=6m;h=9m;\pi=3.14 \\ A_{cylinder}=2\times3.14\times6^2+2\times3.14\times6\times9_{} \end{gathered}$$\begin{gathered} A_{cylinder}=6.28\times36+6.28\times54 \\ =226.08+339.12 \\ =565.2m^2 \end{gathered}$

Hence the surface area of the cylinder is 565.2m²