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What will be the diameter of the sphere, if a cone of height 20 cm and radius of base 5 cm is made up of modeling clay, which is reshaped by a child into the form of a sphere?

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10cm

15cm

25cm

45cm

answer is A.

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Detailed Solution

Given,
A cone of height 20 cm and radius of base 5.
We have to find the diameter of the sphere.

Volume of a cone = 13 π r 2 h, where r is the radius of the base, and h is the height of the cone . Volume of a sphere = 43 π 3, where r is the radius of the sphere .

Suppose the radius of the sphere is R.
Note that,
The volume of sphere= Volume of a cone

∴ 43 π R 3 = 13 π r 2 h ⇒ R 3 = π r 2 h × 3 3 × 4 π ⇒ R 3 = r 2 h 4

Putting the values,

⇒ R 3 = 5 × 5 × 20 4 ⇒ R 3 = 125 ⇒ R = 1253 ⇒ R = 5 cm

Calculating the diameter of the sphere,

∴ Diameter of the sphere = 2 R ⇒ Diameter of the sphere = 2 × 5 = 10 cm

So, the diameter of the sphere is 10 cm.
Therefore, option 1 is correct.

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