# Find the volume of a solid in the form of a right circular

Question:

Find the volume of a solid in the form of a right circular cylinder with hemi-spherical ends whose total length is 2.7 m and the diameter of each hemi-spherical end is 0.7 m.

Solution:

$=\frac{1}{2} \times 0.7$

$=\frac{7}{20} \mathrm{~m}$

Total length = 2.7 m.

Height of cylinder

$=2.7-2 \times \frac{7}{20}$

$=2 \mathrm{~m}$

Volume of two hemispheres

$=2\left(\frac{2}{3} \pi r^{3}\right)$

$=\frac{4}{3} \pi r^{3}$

$=\frac{4}{3} \times \frac{22}{7} \times\left(\frac{7}{20}\right)^{3}$

$=\frac{4}{3} \times \frac{22}{7} \times \frac{343}{800}$

$=0.1797 \mathrm{~m}^{3}$

Volume of cylinders

$=\pi r^{2} h$

$=\frac{22}{7} \times\left(\frac{7}{20}\right)^{2} \times 2$

$=0.77 \mathrm{~m}^{2}$

Hence,

Volume of solid = 0.1797+0.77 = 0.95 m3