Exercise 21 Page 852

The volume of a hemisphere is half the volume of a sphere with the same radius.

2712.3cm^3

Practice makes perfect

A hemisphere is the name of a solid that is half of a sphere.

Therefore, the volume of a hemisphere with radius r is half the volume of a sphere with radius r. Volume of a Hemisphere [0.8em] V=1/2(4/3π r^3) ⇔ V=2/3π r^3 To use this formula we first need to calculate the radius. Consider the given fact that the diameter is twice the radius of the circle. d=2r We can substitute 21.8 for d in the above formula and solve for the radius r.

d=2r

Substitute

d= 21.8

21.8=2r

DivEqn

.LHS /2.=.RHS /2.

10.9=r

RearrangeEqn

Rearrange equation

r=10.9

The radius measures 10.9cm. We can substitute this value in the formula for the volume of a hemisphere and simplify.

V=2/3π r^3