Question

What is the volume of a hemisphere with a diameter of 51.8 inches rounded to the nearest 10th of a cubic inch?

Answer 1

Answer:

volume of a hemisphere ≈ 36369.5 in³

Step-by-step explanation:

To find the formula for calculating the volume of a hemisphere, we will follow the steps below:

write the formula for calculating the volume of a hemisphere.

volume of a hemisphere = volume of a sphere ÷2

                                        = $\frac{4}{3}$πr³   ÷   2

                                        =$\frac{2}{3}$ πr³

where r is the radius

from the question given, diameter = 51.8 inches

but diameter = 2r , this implies that r = $\frac{d}{2}$    hence   r = $\frac{51.8}{2}$ = 25.9 inches

π is a constant and is ≈ 3.14

we can now proceed to insert the values into the formula

volume of a hemisphere    =$\frac{2}{3}$ πr³

                                                =$\frac{2}{3}$ × 3.14 ×25.9³

                                                =$\frac{2}{3}$ × 3.14×17373.979

                                                 ≈36369.5 in³ to the nearest tenth cubic inch.

volume of a hemisphere ≈ 36369.5 in³