Volume of a hemisphere

Half a sphere is called a hemisphere.

\(Volume\,of\,hemisphere = \frac{1}{2}volume\,of\,a\,sphere\)

Example

A glass bowl is in the shape of a hemisphere with diameter 13cm.Trisha will fill the bowl with water so that she can use it for floating candles. What is the maximum amount of water the glass bowl can hold?

Give your answer in millilitres correct to 2 significant figures.

Answer

Diameter = 13cm therefore the radius = \(13 \div 2 = 6.5cm\).

Volume of Sphere = \(V = \frac{4}{3}\pi {r^3}\)

\(= \frac{4}{3} \times \pi \times {(6.5)^3}\)

\(= 1150.346...\)

\(Volume\,of\,hemisphere = \frac{1}{2}volume\,of\,sphere\)

\(= 0.5 \times 1150.346...\)

\(= 575.173...c{m^3}\)

Since \(1c{m^3} = 1ml\), the glass bowl can hold 580 ml (to 2 s.f.)

Volume of a prism

Volume of a sphere

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Calculating the volume of a standard solidVolume of a hemisphere