From a solid cylinder whose height is 15 cm and diameter  16 cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid. $[ Use \ \pi =3.14]$

Given: Diameter of the cylinder and the cone $=16$ cm and the height of the of the cylinder and cone$=15$cm.

To do: To find the total curved surface area of the remaining solid after the conical cavity is hollowed out.

Solution: 

As given height of the cylinder h$=15$ cm

Diameter of the cylinder $=16$ cm

$\therefore$ Radius of the cylinder $\frac{Diameter}{2}\ =\ \frac{16}{2}=8$ cm

 $\because$ Diameter and height of the cylinder and cone are same.

$\therefore$ Slant height of the cone, $l=\sqrt{h^{2} +r^{2}}$

$=\sqrt{15^{2} +8^{2}}$

$=\sqrt{225+64}$

$=\sqrt{289}$

$=17\ $ cm

Total surface area of the remaining solid$=$Curved surface area of the cylinder$+$Area of the base$+$Curved surface area of the cone

$=2\pi rh+\pi r^{2} +\pi rl$

$=\pi r( 2h+r+l)$

$=3.14\times 8( 2\times 15+8+17)$

$=25.12( 30+25)$

$=25.12\times 55$

$=1381.6\ cm^{2}$

Therefore, total surface area of the remaining solid is $1381.6\ cm^{2}$

Tutorialspoint

Simply Easy Learning

Updated on: 10-Oct-2022

108 Views

Kickstart Your Career

Get certified by completing the course

Get Started