Question

A cylinder of radius 10cm and height 21cm is melted and recast into a certain number of cones of radius 3cm and height 7cm. Find the number of cones

Answer 1

Step-by-step explanation:

We have

Height of solid circular cylinder= 10cm

Radius of the base = 6cm

volume of the remaining solid = volume of the cylinder - volume of the cone

Volume of remaining solid=(πr

2

h)−

3

1

πr

2

h

={π×6

2

×10−

3

1

×π×6

2

×10}cm

3

=(360π−120π)cm

3

=240πcm

3

slant height of the cone

=OC=

OC

2

+O

′

C

2

=

10

2

+6

2

=2

34

cm

Whole surface area = curved surface area of the cylinder + area of the base the cylinder + curved surface area of cone

={2π×6×10+π×6

2

+π×6×2

34

}cm

2

=(156+12

34

)πcm

2