Question

find the volume of a hemisphere when the diameter is 24 cm. Leave answer in terms of Pi

Answer 1

hello

to solve this problem, we have to use the formula of volume of a hemisphere

$\begin{gathered} V_{\text{hemisphere}}=\frac{2}{3}\pi r^3 \\ r=\text{radius} \end{gathered}$

in this question, we are given the value of diameter, we have to use this information to find the radius of the hemisphere

$\begin{gathered} \text{radius}=\frac{\text{diameter}}{2} \\ \text{diameter}=24\operatorname{cm} \\ \text{radius}=\frac{24}{2} \\ \text{radius}=12\operatorname{cm} \end{gathered}$

let's proceed and insert the value of the radius into the formula above

$\begin{gathered} V_{\text{hemisphere}}=\frac{2}{3}\pi r^3 \\ r=12\operatorname{cm} \\ V_{\text{hemisphere}}=\frac{2}{3}\times\pi\times12^3 \\ V_{\text{hemisphere}}=\frac{2}{3}\times1728\times\pi \\ V_{\text{hemisphere}}=1152\pi cm^3 \end{gathered}$

from the calculation above, the volume of the hemisphere is equal to 1152pi cm^3