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Question
The dimensions of a metallic cuboid are 44 cm × 42 cm × 21 cm. it is molten and recast into a sphere. Find the surface area of the sphere.
Solution
The volume of cuboid = l × b × h
= (44 × 42 × 21) cm3
= 38808 cm3
Since, the metallic cuboid is molten and into a sphere,
volume of sphere = volume of cuboid
∴ volume of sphere = 38808 cm3
But, volume of sphere = `4/3 pir^3`
∴ `4/3 pir^3` = 38808
∴ `r^3 = 38808 xx 3/4 xx 7/22`
∴ r3 = 21 × 21 × 21
∴ r = 21 cm
∴ surface area of spher = 4πr2
= `4 xx 22/7 xx(21)^2`
= 5544 cm2
∴ the surface area of the sphere is 5544 cm2.
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