Question

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Answer 1

Answer:

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Answer. The number of cones that can be made are 9. Thus, volume of the cylinder = sum of the volumes of n cones. Therefore, 9 cones can be made.

Let R be the radius and H be the height of the cylinder and let rand h be the radius and height of the cone respectively. Then,

3r=2R

and H:h=4:3 ......(i)

⇒

h

H

=

3

4

⇒3H=4h .......(ii)

Let n be the required number of cones which can be made from the materials of the cylinder. Then, the volume of the cylinder will be equal to the sum of the volumes of n cones. Hence, we have

πR

2

H=

3

n

πr

2

h

⇒3R

2

H=nr

2

h

⇒n=

r

2

H

3R

2

H

=

r

2

h

3×

4

9r

2

×

3

4h

[∵ From (i) and (ii), R=

2

3r

and H=

3

4h

]

⇒n=

3×4

3×9×4

⇒n=9

Hence, the required number of cones is 9.

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Answer 2

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