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प्रश्न
A solid piece of metal in the form of a cuboid of dimensions 11 cm × 7 cm × 7 cm is melted to form 'n' number of solid spheres of radii `7/2` cm each. Find the value of n.
उत्तर
We know that, volume of cuboid = l × b × h
Volume of sphere = `4/3 πr^3`
Given, l = 11 cm
b = 7 cm,
h = 7 cm and r = `7/2` cm
Here, volume of cuboid = n × volume of sphere
or, 11 × 7 × 7 = `n xx 4/3 π (7/2)^3`
or, 11 × 7 × 7 = `n xx 4/3 xx 22/7 xx 7/2 xx 7/2 xx 7/2`
or, n = `(11 xx 7 xx 7 xx 3 xx 7 xx 2 xx 2 xx 2)/(4 xx 22 xx 7 xx 7 xx 7)`
or, n = 3
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