Question

two cones of the same size are put together so that thier circular faces are joined. Draw the shape thus formed .

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Answer 1

Answer:

place the pointy part at the outer side so thet the bace will be joined

Answer 2

Answer:

Solution

Let h be the height of two given cones of base radii r

1

and r

2

respectively.

Further, let R be the radius of the cylinder.

It is given that the cylinder is also of height h.

It is also given that the cylinder is casted out of both cones.

Therefore, volume of the cylinder = sum of the volumes of two cones

We know that, volume of a cylinder =πr

2

h and volume of a cone =

3

1

πr

2

h

∴ πR

2

h=

3

1

πr

1

2

h+

3

1

πr

2

2

h

⇒πR

2

h=

3

1

πh(r

1

2

+r

2

2

)

⇒R

2

=

3

1

(r

1

2

+r

2

2

)

⇒R=

3

(r

1

2

+r

2

2

)

[Hence proved]

Explanation:

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