Question

A cylindrical vessel with internal diameter $10\text{cm}$ and height $10.5\text{cm}$ is full of water. A solid cone of base diameter $7\text{cm}$ and height $6\text{cm}$ is completely immersed in water. Find the value of water:

(i) displaced out of the cylinder

(ii) left in the cylinder. (Take $\pi =\frac{22}{7}$)

Answer 1

Height of cylinder, $H=10.5\text{cm}$

Radius of cylinder$=R=\frac{D}{2}$

$=\frac{10}{2}\text{cm}$

$=5\text{cm}$

Volume of cylinder $=\pi R^{2}H$

$=\frac{22}{7}\times 5^2\times 10.5{\text{cm}}^3$

$=825{\text{cm}}^3$

Height of cone, $h=6\text{cm}$

Radius of cone$=r=\frac{D}{2}$

$=\frac{7}{2}\text{cm}$

$=3.5\text{cm}$

Volume of cone$=\frac{1}{3}\pi r^{2}h$

(i).

Volume of water displaced$=$ Volume of cone

$=\pi \times {3.5}^2\times 6{\text{cm}}^3$

$=231{\text{cm}}^3$

(ii)

Volume of Water left in the vessel= Volume of cylinder-Volume of cone

$V=\pi r^{2}h-\frac{1}{3}\pi r^{2}h$

$V=(825-231){\text{cm}}^3$

$V=594{\text{cm}}^3$