Question

Please see image below. need help solving. need volume in cubic feet

Answer 1

The volume of a cylinder is equal to the product of the area of the circular base and the height of the cylinder:

`V=Bh`

Where

B represents the area of the circular base

h represents the height of the cylinder

The area of a circle can be calculated following the formula:

`B=\pi r^2`

You can rewrite the formula for the volume using the formula of the area:

`V=\pi r^2\cdot h`

The cylinder described in the exercise has a height of h=30in, and a diameter of d=4ft

The radius is half the diameter so that:

`\begin{gathered} r=(d)/(2) \\ r=(4)/(2) \\ r=2ft \end{gathered}`

Note that the height is expressed in inches and the radius is expressed in feet, to be able to calculate the volume, both dimensions should be expressed using the same unit.

Since we have to provide the final answer in cubic feet, what's best is to convert the height from inches to feet:

h=30in

We know that 1ft corresponds to 12in, to pass 30in to feet, you have to divide the value by 12:

`\begin{gathered} 1ft=12in_{} \\ \text{xft}=30in \\ (1)/(12)=(x)/(30) \\ 30\cdot(1)/(12)=x \\ x=2.5ft \end{gathered}`

30 inches is equal to 2.5ft

Now what's left is to determine the volume of the cylinder with height 2.5ft and r=2ft:

`\begin{gathered} V=\pi r^2\cdot h \\ V=\pi(2^2)\cdot2.5 \\ V=\pi\cdot4\cdot2.5 \\ V=10\pi ft^3 \end{gathered}`

The volume of the cylinder is 10π ft³