Question

In the adjoining figure, the bottom of the glass has a hemispherical raised portion. If the glass is filled with orange juice, then the quantity of juice which a person will get is

• A. $135\pi c{m}^3$
• B. $117\pi c{m}^3$
• C. $99\pi c{m}^3$
• D. $36\pi c{m}^2$

Answer 1

The correct option is B $117\pi c{m}^3$

Volume of the net juice in the cylinder $=$ Volume of cylinder $-$ Volume of hemisphere
Volume $=\left(\pi \right)r^{2}h-\frac{2}{3}\times \left(\pi \right)\times r^3$

$=\left[\right(\pi )\times 9\times 15]-\frac{2}{3}\times \left(\pi \right)\times 3^3$

$=\left(\pi \right)\times [135-18]=117\left(\pi \right)$

Hence, option B.