Question 147

How many hemispherical balls can be made from a cylinder 56 cm high and 12 cm diameter, when every ball being 0.75 cm in radius ?

Solution

Radius of cylinder = $$r=6$$ cm and height = $$h=56$$ cm

=> Volume of cylinder = $$\pi r^2h$$

= $$\pi\times(6)^2\times56=2016\pi$$ $$cm^3$$

Radius of hemisphere = $$R=0.75$$ cm

=> Volume of hemisphere = $$\frac{2}{3}\pi (R)^3$$

= $$\frac{2}{3}\pi\times(0.75)^3=0.28125\pi$$ $$cm^3$$

$$\therefore$$ Number of balls made = $$\frac{2016\pi}{0.28125\pi}=7168$$

=> Ans - (D)

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