Question

From a solid cylinder whose height is 40 cm and diameter 18 cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid

Answer 1

Given :

Height of the solid cylinder = 40 cm

Diameter of the solid cylinder = 18 cm

Height of the conical cavity to be hollowed out = 40 cm ( since cone is of same height as cylinder )

Diameter of the conical cavity = 18 cm

To Find :

The total surface area of the solid remaining after the hollowed conical cavity is taken out  = ?

Solution :

The surface area of remaining solid will be :

= curved surface area of cone + curved surface area of cylinder + area of upper face of the cylinder

= $\pi r l + 2 \pi r h + \pi r^2$      

(Here , r is radius of cylinder and cone , l is slant height of cone , h is height of cylinder and cone .)

Slant height of cone is :

l = $\sqrt{r^ +h^2}$

 =$\sqrt{9^2 + 1600 ^2}$

 = 41 cm

So , the total surface area of remaining solid is :

= $\pi \times 9 \times 41 + 2 \times \pi \times 9 \times 40 + \pi (9)^2$

=$\pi ( 369 + 720 + 81 )$

=$1170 \pi cm^2$

= 3673.8 $cm^2$

Hence , the area of the remaining solid is 3673.8 $cm^2$ .

Answer 2

Step-by-step explanation:

this is your answer

hope this helps you