Question : A cylinder has some water in it at a height of 16 cm. If a sphere of radius 9 cm is put into it, then find the rise in the height of the water if the radius of the cylinder is 12 cm.
Option 1: 8 cm
Option 2: 6 cm
Option 3: 8.75 cm
Option 4: 6.75 cm
Correct Answer: 6.75 cm
Solution :
According to the question
⇒ $\frac{4}{3} \pi r^{3}$ = $\pi r^{2}$ × h
⇒ h = $\frac{\frac{4}{3} \pi r^{3}}{\pi r^{2}}$
⇒ $\frac{\frac{4}{3} \pi (9)^{3}}{\pi (12)^{2}}$
⇒ $\frac{\frac{4}{3} × 729}{3 × 144}$
⇒ $\frac{\frac{4}{3} × 729}{3 × 144}$ = $\frac{2916}{432}$
⇒ $\frac{81}{12}$ = 6.75
Rise in height = 6.75 cm
Hence, the correct answer is 6.75 cm.
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