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A solid cone of radius 5 cm and height 8 cm is melted and made into small spheres of radius 0.5 cm. Find the number of spheres formed.

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Answer

Let no. of small spheres formed be n.

Given,

Radius of cone (R) = 5 cm,

Height of cone (H) = 8 cm,

Radius of sphere (r) = 0.5 cm.

Since, cone is melted and recasted into n spheres.

∴ Volume of cone = n × Volume of spheres

⇒13πR2H=n×43πr3⇒R2H=n×4r3⇒n=R2H4r3⇒n=52×84×(0.5)3⇒n=25×84×0.125⇒n=2000.5⇒n=400.\Rightarrow \dfrac{1}{3}πR^2H = n \times \dfrac{4}{3}πr^3 \\[1em] \Rightarrow R^2H = n \times 4r^3 \\[1em] \Rightarrow n = \dfrac{R^2H}{4r^3} \\[1em] \Rightarrow n = \dfrac{5^2 \times 8}{4 \times (0.5)^3} \\[1em] \Rightarrow n = \dfrac{25 \times 8}{4 \times 0.125} \\[1em] \Rightarrow n = \dfrac{200}{0.5} \\[1em] \Rightarrow n = 400.

Hence, 400 spheres will be formed.

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