Question

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

Answer 1

Given, height of cylinder, ${}^{\prime }{h}^{\prime }=2.4cm$
Radius of base, ${}^{\prime }{r}^{\prime }=0.7cm$
And slant height $l=\sqrt{h^2+r^2}$
$=\sqrt{(2.4{)}^2+(0.7{)}^2}$
$=\sqrt{5.76+0.49}$
$=\sqrt{6.25}$
$=2.5cm$

Total surface area of the remaining solid = CSA of cylinder + CSA of cone + Area of top
$=2\pi rh+\pi rl+\pi r^2$
$=\frac{22}{7}\times 0.7[2\times 2.4+2.5+0.7]$
$=2.2[4.8+2.5+0.7]$
$=2.2\times 8=17.6c{m}^2$