Video Transcript
Work out the volume of the
hemisphere, giving your answer to two decimal places.
To work out the volume of the
hemisphere, let’s first recall the formula for the volume of a sphere. That’s four over three 𝜋𝑟 cubed,
where 𝑟 is the radius of the sphere. Now, a hemisphere, by definition,
is exactly one-half of a sphere. And so its volume must be half that
of the sphere with the same radius. That’s two over three 𝜋𝑟
cubed.
We see that our diagram includes a
great circle with radius 8.3 meters. And since the radius of the great
circle is also the radius of the corresponding sphere, and therefore the same as the
radius of the hemisphere, we have that the volume of the hemisphere is equal to two
over three 𝜋 times 8.3 cubed. That’s two over three 𝜋 times
571.787. This evaluates to 1197.5478 and so
on, which to two decimal places is 1197.55. Hence, to two decimal places, the
volume of the hemisphere of radius 8.3 meters is 1197.55 cubic meters.
We note finally that we could’ve
worked this out by using the formula for the volume of the whole sphere and halving
our result at the end.
