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Question 104

A cylindrical bar of height 1 metre and base radius 0.75 metres is melted and cast as a sphere and cast as a sphere. Then the diameter of a sphere in meters is

Solution

Solution:

Volume of Cylindrical bar = Volume of cast sphere

$$\pi\ r^2\ h\ =\ \frac{4}{3\ }\pi\ R^3$$

$$\pi\ \left(0.75\right)^2\ 1\ =\ \frac{4}{3\ }\pi\ R^3$$

$$\left(\frac{3}{4}\right)^2\ =\ \frac{4}{3}R^3$$

$$\left(\frac{3}{4}\right)^2\ \ .\ \frac{3}{4}=\ R^3$$

$$\left(\frac{3}{4}\right)^3=\ R^3$$

R= 3/4 m

D = 2R = 3/2 = 1.5m

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