Question

Match the correct expression for volume of the following 3D - shapes.

• A. $\frac{4}{3}\pi r^3$
• B. $\frac{2}{3}\pi r^3$
• C. $\pi r^{2}h$
• D. $a^3$

Answer 1

Let length of each side of the cube is ${}^{\prime }{a}^{\prime }$ units.

Volume of cube = ${\text{Side}}^3$

$\therefore$ Volume of the cube = $a^3$


Let radius of the cylinder is ${}^{\prime }{r}^{\prime }$ units and height of the cylinder is ${}^{\prime }{h}^{\prime }$ units.

$\text{Volume of cylinder}=\text{base area}\times \text{height}=\pi r^2\times h=\pi r^{2}h$
$\therefore$ Volume of the cylinder = $\pi r^{2}h$


Let radius of the sphere is ${}^{\prime }{r}^{\prime }$ units.
$\therefore$ Volume of the sphere = $\frac{4}{3}\pi r^3$


Let radius of the hemisphere is ${}^{\prime }{r}^{\prime }$ units.
Volume of the hemisphere
$=\frac{1}{2}\times \text{Volume of the sphere}=\frac{1}{2}\times \frac{4}{3}\pi r^3=\frac{2}{3}\pi r^3$