Question

plz solve this questions
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Answer 1

Answer:

Correct option is

A

1:7

Let the height and radius of the given cone be H and R respectively.

The cone is divided into two parts by drawing a plane through the mid point of axis of cone and parallel to the axis of cone and parallel to the base.

One part is a smaller cone and the other part is a frustum of cone.

Therefore, OC=CA=

2

H

cm

Let the radius of smaller cone be r cm

In △OCD and △OAB,

∠OCD=∠OAB(90

0

)

∠COD=∠AOB (common)

∴△OCD∼△OAB (AA similarity)

⇒

OC

OA

=

CD

AB

=

OD

OB

(By CPCT)

∴

2

H

H

=

r

R

⇒R=2r

Volume of smaller cone:

=

3

1

π(CD)

2

×OC

=

3

1

πr

2

×

2

H

=

6

πr

2

H

cm

3

Volume of cone:

=

3

1

π(AB)

2

×OA

=

3

1

×π×R

2

×H

=

3

πR

2

H

cm

3

=

3

π(2r)

2

H

cm

3

=

3

4πr

2

H

cm

3

Volumeofcone

Volumeofsmallercone

=

3

4πr

2

H

6

πr

2

H

=

6

1

×

4

3

=

8

1

∴ Ratio of volume of upper part to the cone is 1:8