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# A hollow right prism of equilateral triangular base of side 4cm is filled with w...

### Question

A hollow right prism of equilateral triangular base of side 4cm is filled with water up to a certain height. If a sphere of radius $$\frac{1}{2}$$cm is immersed in the water, then the rise of water is

### Options

A) 1cm

B) $$\sqrt{\frac{3\pi}{24}}$$

C) $$\frac{\pi}{24\sqrt{3}}$$

D) 24$$\sqrt{3}$$

### Explanation:

The rise of water is equivalent to the volume of the sphere of radius $$\frac{1}{2}$$cm immersed x $$\frac{1}{\text{No. of sides sq. root 3}}$$

Vol. of sphere of radius = 4$$\pi$$ x $$\frac{1}{8}$$ x $$\frac{1}{3}$$ - ($$\frac{1}{2}$$)3

= $$\frac{1}{8}$$

= $$\frac{\pi}{6}$$ x $$\frac{1}{4\sqrt{3}}$$

= $$\frac{\pi}{24\sqrt{3}}$$

## Dicussion (1)

• The rise of water is equivalent to the volume of the sphere of radius $$\frac{1}{2}$$cm immersed x $$\frac{1}{\text{No. of sides sq. root 3}}$$

Vol. of sphere of radius = 4$$\pi$$ x $$\frac{1}{8}$$ x $$\frac{1}{3}$$ - ($$\frac{1}{2}$$)3

= $$\frac{1}{8}$$

= $$\frac{\pi}{6}$$ x $$\frac{1}{4\sqrt{3}}$$

= $$\frac{\pi}{24\sqrt{3}}$$