Question

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 1

Given that,
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

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 that
Total surface area of cylinder = 2πr(r+h) ,
So,
Total surface area of this solid cylinder= 2× 22/7 × 3.5( 3.5 + 15)
Total surface area of this solid cylinder= 22× 18.5 = 407 cm^2

And
Area of base of cone = πr2,
So,
Area of base of both cones = 2×πr^2

Area of base of both cones = 2×227×3×3
Area of base of both cones =3967
= 56.57 cm2

And

Slant height of cone
l =h^2 + r^2
=4^2 +3^2 = 16 + 9 = 25 = 5 cm

we know that,
curved surface area of cone =πrl,
So,
Curved surface area of both cones
= 2×πrl
= 2×227 ×3×5
=6607 = 94.28 cm^2
Then,
Surface area of remaining solid cylinder = 407 cm2- 56.57 cm2+ 94.28 cm2
= 444.71 cm2