CMAT 2022 Question 3

Question 3

A copper wire having length of 243m and diameter 4 mm was melted to form a sphere. Find the diameter of the sphere :

Solution

Volume of copper wire melted will be equal to volume of sphere.

Volume of copper wire = Area $$\times\ $$ length = $$\pi\ \left(\frac{2}{10}\right)^2\times\ 24300\ cm^3$$

Let the radius of sphere be r

$$\frac{4}{3}\pi\ r^{3\ \ }=\ \pi\ \left(\frac{2}{10}\right)^2\times\ 24300\ cm^3$$

$$r^3$$ = 729

r = 9 cm

Diameter of sphere = 2(9) = 18 cm

Answer is option B.



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