Video Transcript
Find, to the nearest tenth, the volume of a hemisphere given that the circumference of its great circle is 82𝜋.
A hemisphere is half a sphere, and its volume can be calculated using the formula two-thirds 𝜋𝑟 cubed, where 𝑟 is the radius of the hemisphere. The great circle is the base of the hemisphere, as shown in the diagram. The circumference of any circle can be calculated using the formula 𝜋𝑑. As we’re told the circumference of the great circle is 82𝜋, then this is equal to 𝜋𝑑. Dividing both sides of this equation by 𝜋 gives us 82 is equal to 𝑑. This means that the diameter of the great circle is 82 units.
The radius is half the diameter, so this can be calculated by dividing 82 by two. This is equal to 41. We can now calculate the volume of the hemisphere by multiplying two-thirds by 𝜋 by 41 cubed. Typing this into the calculator gives us 144347.804 and so on. As we need to round to the nearest tenth, the deciding number is the zero in the hundredths column. If the deciding number is less than five, we round down. The volume of the hemisphere to the nearest tenth is 144347.8. In this question, we don’t know the specific units.
