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What is the volume of a hemisphere with radius 3 ft? What is the volume of a hemisphere with diameter 13 cm?

Sagot :

The volume of a sphere is given by

[tex]V_s=\frac{4}{3}\pi r^3[/tex]

Since a hemisphere is half sphere, its volume is given by

[tex]\begin{gathered} V_{}=\frac{4}{6}\pi r^3 \\ \text{which is equivalent to} \\ V_{}=\frac{2}{3}\pi r^3 \end{gathered}[/tex]

where r is the radius.

Case a.

In this part r=3 ft, then by substituting this values into our last formula we get

[tex]V=\frac{2}{3}(3.1416)(3^3)[/tex]

which gives

[tex]V=56.55ft^3[/tex]

Case b.

In this part r=(13/2) cm, then by substituting this values into our last formula we get

[tex]V=\frac{2}{3}(3.1416)(6.5^3)[/tex]

which gives

[tex]V=287.59cm^3[/tex]