Question

The circumference of the base of a circular cylinder is $6\pi $ cm. The height of the cylinder is equal to the diameter of the base. How many liters of water can it hold?
A. $0.54\pi $ liters
B. $0.6\pi $ liters
C. $0.5\pi $ liters
D. $0.4\pi $ liters

Answer 1

Hint – We will start solving the question by writing down the given information. By using it we will draw a figure and find out the other required values. Then we will use the formula of the Volume of the Cylinder, i.e., $\pi \times radiu{s^2} \times height$, which will give us our final answer.

Complete step-by-step answer:
It is given in the question that the circumference of the base of a circular cylinder is $6\pi $ cm and its height is equal to the diameter of the base of the cylinder.

So by using this, we can make a figure, which is as follows:

Given that,
Circumference of the base of the cylinder $ = 6\pi cm$
We know that circumference of the cylinder is $2\pi r$, where $r$ is the radius.
$
  \therefore 2\pi r = 6\pi \\
   \Rightarrow 2r = 6 \\
   \Rightarrow r = \dfrac{6}{2} \\
   \Rightarrow r = 3cm \\
 $
Thus, Radius $\left( r \right)$ = 3 cm.

Now, we know that,
$
  Radius = \dfrac{{Diameter}}{2} \\
   \Rightarrow Diameter = 2 \times Radius \\
 $

Therefore, Diameter $ = 2 \times 3$
                                     $ = 6cm$

Also, it is given in the question that the height of the cylinder is equal to the diameter of the base, therefore,
Height of the cylinder $\left( h \right)$ = 6 cm

Now,
Volume of the cylinder $ = \pi {r^2}h$
                                          $
   = \pi \times {\left( 3 \right)^2} \times 6 \\
   = \pi \times 9 \times 6 \\
 $
                                          $ = 54\pi $ml.
                                          $ = \dfrac{{54\pi }}{{1000}}$ lt.
                                          $ = 0.054\pi $lt.
Hence, the cylinder can hold $0.054\pi $ liters of water.
Thus, option A is the right answer.

Note - A cylinder is a closed solid that has two parallel bases joined by a curved surface, at a fixed distance. While solving these questions, all the formulas should be known, otherwise the question could not be solved because this is the only way to solve it.