Question

help me find the volume and area of this figure step by step pleasefyi the answer key my teacher gave me says that the surface area=391.57 ft^2 and the volume=169.65 ft^3

Answer 1

The volume of the shape

We have a cylinder that is cut into two. Its external radius is 5ft, while its internal radius is 4ft.

External radius = internal radius + thickness

`\begin{gathered} \text{External radius = 4ft + 1ft } \\ =\text{ 5ft} \end{gathered}`

Internal radius = 4ft (given)

Recall that the volume(V) of a full cylinder is:

`V\text{ = }\pi r^2h`

Since the cylinder is cut into two, the volume(V) is:

`V\text{ = }(\pi r^2h)/(2)`

height (h) = 12ft (given)

The volume of the shape:

`\begin{gathered} =\text{ Volume of cylinder with a radius of 5ft - Volume of cylinder with a radius of 4ft} \\ =\text{ }\frac{\pi\text{ }*5^2\text{ }*\text{ 12}}{2}\text{ - }\frac{\pi\text{ }*4^2\text{ }*\text{ 12}}{2} \\ =\text{ 471.239 - }301.593 \\ =169.65ft^3 \end{gathered}`