Question

From a solid cylinder of height 20 cm and diameter 12 cm, a conical cavity of height 8 cm and radius 6 cm is hollowed out. Find the total surface area of the remaining solid.
$[Use\pi =\frac{22}{7}]$

Answer 1

The remaining solid, after removing the conical cavity, can be drawn as,

Height of the cylinder, $h_1$ = 20 cm

$\therefore$ Radius of the cylinder, $r=\frac{12cm}{2}=6m$

Height of the cone, $h_2$ = 8 cm

Radius of the cone, r = 6 cm

Total surface area of the remaining solid

$\Rightarrow$ Areas of the top face of the cylinder + curved surface area of the cylinder + curved surface area of the cone
Slant height of the cone,
$I=\sqrt{(8cm{)}^2+(6cm{)}^2}$
$=\sqrt{64c{m}^2+36c{m}^2}$
$=\sqrt{100}cm$
= 10 cm
Curved surface are of the cone = $\pi rl=\frac{22}{7}\times 6cm\times 10cm=\frac{1320}{7}c{m}^2$
Curved surface are of the cylinder = $=2\pi rh=2\times \frac{22}{7}\times 6cm\times 10cm=\frac{5280}{7}c{m}^2$
Area of the top face of the cylinder = $=\pi r^2=\frac{22}{7}\times (6cm{)}^2=\frac{792}{7}c{m}^2$
$\therefore$ Total surface area of the remaining soild $=(\frac{1320}{7}+\frac{5280}{7}+\frac{792}{7})c{m}^2$
$=\frac{7392}{7}c{m}^2$
$=1056c{m}^2$