Question 27

Three spherical balls of radius 1 cm, 2 cm and 3 cm are melted to form a single spherical ball. In the process, the loss of material is 25%. The radius of the new ball is

Solution

material lost = 25 % = $$ \frac{1}{4} $$

remaining = $$ 1 - \frac{1}{4} = \frac{3}{4} $$

volume of sphere = $$ \frac{4}{3} \pi r^3 $$

volume of new ball = $$ \frac{3}{4} \times \frac{4}{3} \pi ( r1^3 + r2^3 + r3^3) $$

= $$ \pi ( 1^3 + 2^3 + 3^3 ) $$

= $$ 36 \pi cm^3 $$

$$ \frac{4}{3} \pi r^3 = 36 \pi $$

solving r = 3 cm

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