The height of a cylinder is three times the radius of its base. If the area of the base is 616 cm², then what is the capacity (in litres) of the cylinder ? Use $\pi =\frac{22}{7}$

The correct option is 25.872.

Step 1: Find the radius of the base of the cylinder

Let the radius of the base of the cylinder be $r$ cm and its height be $h$ cm.

The base of a cylinder is a circle. The area of the base is given as 616 cm².

Area of base = $\pi r^2$

$\frac{22}{7}\times r^2=616$

$r^2=\frac{616\times 7}{22}$

$r^2=28\times 7=196$

$r=\sqrt{196}=14$ cm

Step 2: Find the height of the cylinder

We are given that the height of the cylinder is three times the radius of its base:

$h=3\times r$

$h=3\times 14=42$ cm

Step 3: Calculate the volume (capacity) of the cylinder

Volume of a cylinder = Area of base $\times$ height

$\text{Volume}=616\times 42$

$\text{Volume}=25872$ cm³

Step 4: Convert the volume from cubic centimeters to litres

Since 1 litre = 1000 cm³, we divide the volume in cm³ by 1000:

$\text{Capacity in litres}=\frac{25872}{1000}=25.872$ litres

Thus, the capacity of the cylinder is 25.872 litres.