Question

A grain tank on a farm is composed of a storage portion in the shape of a cylinder anda cone-shaped dispensing area at the bottom. The bottom cone portion has a slantheight of 5.5 feet. The entire exposed surface of the tank is to be painted. What is theapproximate amount of surface area that will receive the painting?8.4 ft12 ft5.5 ft

Answer 1

To fidn the surface area of the grain tank you need to find the area of:

Cylinder (without one of the bases as there are just one base exposed), use the next formula:

`A_1=\pi\cdot r^2+h(2\pi r)`

You have for the given cylinder:

h=12ft

r: as the diameter is 8.4ft the radius is 8.4tf/2=4.2ft

`\begin{gathered} A_1=\pi(4.2ft)^2+12ft(2\pi(\text{4}.2ft)) \\ =17.64\pi ft^2+100.8\pi ft^2 \\ =118.44\pi ft^2 \end{gathered}`

Cone (without the base as the base is not exposed), use the next formula:

`A_2=\pi\cdot r\cdot s`

You have for the given cone:

r= 4.2ft

s= 5.5ft

`\begin{gathered} A_2=\pi(4.2ft)(5.5ft) \\ =23.1\pi ft^2 \end{gathered}`

The entire exposed surface of the tank is:

`\begin{gathered} A_T=118.44\pi ft^2+23.1\pi ft^2 \\ \\ =141.54\pi ft^2 \\ \\ \approx444.66ft^2 \end{gathered}`

The approximate amount of surface area that will receive the painting is 444.66 squared feets