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Mathematics

A solid rectangular block of metal 49 cm by 44 cm by 18 cm is melted and formed into a solid sphere. Calculate the radius of the sphere.

Mensuration

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Answer

Let radius of sphere be r cm.

Since,

A solid rectangular block of metal is melted and formed into a solid sphere.

∴ Volume of rectangular block = Volume of sphere

⇒49×44×18=43πr3⇒38808=43×227×r3⇒r3=38808×214×22⇒r3=9261⇒r3=(21)3⇒r=21 cm.\Rightarrow 49 \times 44 \times 18 = \dfrac{4}{3}πr^3 \\[1em] \Rightarrow 38808 = \dfrac{4}{3} \times \dfrac{22}{7} \times r^3 \\[1em] \Rightarrow r^3 = \dfrac{38808 \times 21}{4 \times 22} \\[1em] \Rightarrow r^3 = 9261 \\[1em] \Rightarrow r^3 = (21)^3 \\[1em] \Rightarrow r = 21 \text{ cm}.

Hence, the radius of sphere = 21 cm.

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