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Mathematics

A cone and a sphere have equal volumes. Their radii are also equal each being 10 cm; the height of the cone is :

  1. 70 cm

  2. 40 cm

  3. 50 cm

  4. 20 cm

Mensuration

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Answer

Let radius of cone and sphere be r cm and height of cone be h cm.

Given,

A cone and a sphere have equal volumes and their radius are equal.

∴ Volume of cone = Volume of sphere

⇒13πr2h=43πr3⇒h=4×3πr33πr2⇒h=4r⇒h=4×10=40 cm.\Rightarrow \dfrac{1}{3}πr^2h = \dfrac{4}{3}πr^3 \\[1em] \Rightarrow h = \dfrac{4 \times 3πr^3}{3πr^2} \\[1em] \Rightarrow h = 4r \\[1em] \Rightarrow h = 4 \times 10 = 40 \text{ cm}.

Hence, Option 2 is the correct option.

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