Question

A cylinder has a radius of 6 cm and a height of 15 cm. A hole of the shape of a cone is bored into one of its ends. If the cone has a radius of 3 cm, find the volume of the remaining solid.

Answer 1

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 ,

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 = 2πr ( r + h ) , So

Total surface area of this solid cylinder = 2× 227 × 3.5 ( 3.5 + 15) ( As we know π = 227 )

Total surface area of this solid cylinder = 22 × 18.5 = 407 cm2

And

Area of base of cone = πr2 , So

Area of base of both cones = 2×πr2

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 = h2 + r2−−−−−−−√ = 42 + 32−−−−−−−√ = 16 + 9−−−−−−√ = 25−−√ = 5 cm

we know curved surface area of cone = πrl , So

Curved surface area of both cones = 2 × πrl

Curved surface area of both cones = 2 × 227 × 3 × 5

Curved surface area of both cones = 6607 = 94.28 cm2

Then

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

Answer 2

1560 cm^3 is the correct answer.