Question

Consider a cylindrical vessel with internal diameter 10 cm and height 10.5 cm is full of water. A solid cone of base diameter 8 cm and height 6 cm is completely immersed in water. Find the volume of water left in the cylinder.

Accepted Answer

Given: Internal diameter of the cylindrical vessel $= 10 c m$

$\Rightarrow$ radius $= 5 c m$

Height of the cylindrical vessel $= 10.5 c m$

Base diameter of the solid cone $= 7 c m$

$\Rightarrow$ radius $= 3.5 c m$

Height of the cone $= 6 c m$

Volume of water displaced out from the cylinder $=$ Volume of the cone

$= \frac{1}{3} {πr}^{2} h$

$=$ $\frac{1}{3} \times \frac{22}{7} \times 3 . 5^{2} \times 6$

$= 77 c m^{3}$

Volume of the cylindrical vessel $=$ ${πr}^{2} h$

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

$= 825 c m^{3}$

Therefore, volume of the water left in the cylinder $=$ Volume of the cylindrical vessel $-$ Volume of the solid cone $= 825 - 77 = 748 c m^{3}$

Therefore, the volume of the water left in cylinder is $748 c m^{3}$

Class	$0 - 100$	$100 - 200$	$200 - 300$	$300 - 400$	$400 - 500$	$500 - 600$	$600 - 700$	$700 - 800$	$800 - 900$	$900 - 1000$
Frequency	$2$	$5$	$x$	$12$	$17$	$20$	$y$	$9$	$7$	$4$

Consider a cylindrical vessel with internal diameter 10 cm and height 10.5 cm is full of water. A solid cone of base diameter 8 cm and height 6 cm is completely immersed in water. Find the volume of water left in the cylinder.

Important Questions on Sample Paper 2

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