# Q : 1     The circumference of the base of a cylindrical vessel is 132 cm and its height is 25 cm. How many litres of water can it hold? ($\small 1000\hspace{1mm}cm^3=1l$)

Given,

Circumference of the base of a cylindrical vessel = $132\ cm$

Height = $h = 25\ cm$

Let the radius of the base of the cylinder be $r\ cm$

Now, Circumference of the circular base of the cylinder = $2\pi r = 132\ cm$

$\\ \Rightarrow 2\times\frac{22}{7}\times r = 12\times11 \\ \\ \Rightarrow r = \frac{12\times7}{4} = 21\ cm$

$\therefore$ The volume of the cylinder = $\pi r^2 h$

$\\ = \frac{22}{7}\times (21)^2 \times25 \\ = 22\times3\times21\times25 \\ = 34650\ cm^3$

Also, $\small 1000\hspace{1mm}cm^3=1l$

$\therefore$ $34650\ cm^3 = \frac{34650}{1000} = 34.65\ litres$

Therefore, the cylindrical vessel can hold $34.65\ litres$ of water.

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