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* radius,r \\ d=2r \\ r=(d)/(2) \\ r=(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*3.14*6^2+2*3.14*6*9_{} \end{gathered}`
`\begin{gathered} A_(cylinder)=6.28*36+6.28*54 \\ =226.08+339.12 \\ =565.2m^2 \end{gathered}`

Hence the surface area of the cylinder is 565.2m²