# The height of cone is 60 cm. If a new cone is cut out parallel to the

| The height of cone is 60 cm. If a new cone is cut out parallel to the base of the original cone such that volume of remaining part (frustum) is times the volume of original cone then find height of the smaller cone.

A. 40 cm

B. 45 cm

C. 35cm

D. 44 cm

### Right Answer is: B

#### SOLUTION

Let volume of larger cone = V

Height of larger cone = 60 cm

So volume of frustum =

Volume of smaller cone = V – =

Let height of smaller cone = h_{1}

As smaller cone is similar to larger cone then We know that if two cones are similar then the ratio of their volumes will be equal to the cube of the ratio of their corresponding heights

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The height of cone is 60 cm. If a new cone is cut out parallel to the