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

Mathematics
JAMB 1978

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
  • A. 1cm
  • B. \(\sqrt{\frac{3\pi}{24}}\)
  • C. \(\frac{\pi}{24\sqrt{3}}\)
  • D. 24\(\sqrt{3}\)
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Correct Answer: Option C
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 \(\frac{1}{4\sqrt{3}}\)

= \(\frac{\pi}{24\sqrt{3}}\)

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