From a solid cylinder of height 15 cm and diameter 7 cm, two conical holes are drilled each of radius 3 cm and height 4 cm. Find the surface area of the remaining solid

Answer :

Given Diameter of cylinder =  7 cm So
Radius of solid cylinder =  3.5 cm
Height of cylinder = 15 cm

And
Radius of cone =  3 cm
Height of cone =  4 cm 

So we form our figure as :

And we want to find surfaced area of reaming solid (  As colored portion of solid cylinder )
So ,

Surface area of remaining solid cylinder =  Total surface area of cylinder -  Area of base of cones +  curved surface area of cones

We know
Total surface area of cylinder =  2$\pi$r ( r + h ) , So

Total surface area of this solid cylinder =  2$\times$ $\frac{22}{7}$ $\times$ 3.5 ( 3.5 + 15)  ( As we know $\pi$ =  $\frac{22}{7}$ )

Total surface area of this solid cylinder =  22 $\times$  18.5  = 407 cm²

And

Area of base of cone  =  $\pi$r² , So
Area of base of both cones  =  2$\times$$\pi$r²

Area of base of both cones  =  2$\times$$\frac{22}{7}$ $\times$ 3 $\times$ 3

Area of base of both cones  = $\frac{396}{7}$  = 56.57 cm²

And

Slant height of cone   l  = $\sqrt{h^2 + r^2}$ = $\sqrt{4^2 + 3^2} = \sqrt{16 + 9} = \sqrt{25} = 5 cm$
we know curved surface area of cone = $\pi$rl , So

Curved surface area of  both cones = 2 $\times$ $\pi$rl 

Curved surface area of  both cones = 2 $\times$ $\frac{22}{7}$  $\times$ 3 $\times$ 5 

Curved surface area of  both cones = $\frac{660}{7}$   = 94.28 cm²

Then

Surface area of remaining solid cylinder = 407 cm² - 56.57 cm² + 94.28 cm²  = 444.71 cm²                         ( Ans )