Question

A cone of height 12 cm and base radlus 3 cm is cut into two parts by a plane parallel to its base at a helght of 8cm from its vertex. The volume of
the larger part will be:

Options
441/3
32/3
76TT/3
641/3
Clear Response​

Answer 1

Answer:

Given, r

1

=12cm,h

1

=20cm,r

2

=3cm,h

2

=?

We know,

r

2

r

1

=

h

2

h

1

∴

3

12

=

h

2

20

∴h

2

=

12

3×20

=5cm

∴ The cut to be made at 5cm from the vertex.

Volume of the frustum=

3

1

πh(r

1

2

+r

2

2

+r

1

r

2

)

=

3

1

×

7

22

×15(12

2

+3

2

+12×3)=

7

110

×(144+9+36)

=

7

110

×189=2,970

∴Volume of the frustum=2,970cm

3

.