Question

From a solid right circular cylinder of a height $2.4$ cm and radius $0.7$ cm, a right circular cone of same height and same radius is cut. Find the total surface area of the remaining solid.

Answer 1

For both Cylinder and Cone : $h=2.4$ cm, $r=0.7$ cm

Total surface area of remaining solid $=$Total surface area of cylinder $-$ Total surface area of cone .... $\left(a\right)$

Total surface area of cylinder $=2\pi r(r+h)$

$=2\pi \times \frac{7}{10}\times (\frac{7}{10}+\frac{24}{10})$

$=\frac{14\pi \times 31}{100}$ ....(1)

Total surface area of cone $=\pi r(r+l)$

$=\pi \times \frac{7}{10}(\frac{7}{10}+\sqrt{h^2+r^2})$

$=\pi \times \frac{7}{10}[\frac{7}{10}+\sqrt{{\left(\frac{24}{10}\right)}^2+{\left(\frac{7}{10}\right)}^2}]$

$=\frac{7\pi }{10}(\frac{7}{10}+\sqrt{\frac{576+46}{100}})$

$=\frac{7\pi }{10}(\frac{7}{10}+\frac{25}{10})$

$=\frac{7\pi }{10}\times \frac{32}{10}...\left(2\right)$

Substituting $\left(1\right)$ and $\left(2\right)$ in $\left(a\right)$,

We get,

Total surface area of remaining solid $=\pi (\frac{434}{100}-\frac{224}{100})$

Total surface area of remaining solid $=6.6c{m}^2$.