Question

Deion measure the volume of a sink basin by modeling it as a hemisphere. Deion measures its diameter to be 28 3/4 inches. Find the sink’s volume in cubic inches. Round your answer to the nearest tenth if necessary.

Answer 1

28.75We are asked to determine the volume of a hemisphere of diameter 28 3/4 in.

A hemisphere is half a sphere therefore, its volume is half the volume of a sphere:

`V=(1)/(2)((4\pi r^3)/(3))=(2\pi r^3)/(3)`

Where "r" is the radius. Since the radius is half the diameter we have that:

`r=(D)/(2)=(28(3)/(4))/(2)`

We will convert the mixed fraction into a standard fraction using the following:

`28(3)/(4)=28+(3)/(4)=28.75`

Substituting in the formula for the radius:

`r=(28.75in)/(2)=14.38in`

Now, we substitute the value of the radius in the formula for the volume:

`V=(2\pi(14.38in)^3)/(3)`

Solving the operations:

`V=6221.3in^3`

Therefore, the volume is 6221.3 cubic inches.