Question

A cylindrical vessel with internal diameter $10cm$ and height $10.5cm$ is full of water. A solid cone of base diameter $7cm$ and height $6cm$ is completely immersed in water. Find the volume of water (i) displaced out of the cylinder (ii) left in the cylinder. (Take $\pi =\frac{22}{7}$)

• A. (i) $77c{m}^3$ and (ii) $748c{m}^3$
• B. (i) $70c{m}^3$ and (ii) $740c{m}^3$
• C. (i) $85c{m}^3$ and (ii) $786c{m}^3$
• D. (i) $88c{m}^3$ and (ii) $797c{m}^3$

Answer 1

The correct option is A (i) $77c{m}^3$ and (ii) $748c{m}^3$

Volume of water displaced $=$ $\text{Volume of cone}$

$=\frac{1}{3}\pi r^{2}h=\frac{1}{3}\times \frac{22}{7}\times \frac{7}{2}\times \frac{7}{2}\times 6$

$=77{cm}^3=0.077$ litre

Volume of water left $=$ $\text{Volume of cylinder}$ $-77{cm}^3$

$=\pi R^{2}H-77$

$=\frac{22}{7}\times 5\times 5\times 10.5-77$

$=825-77$

$=748{cm}^3=0.748$ litre