Question

The circumference of 1 cm thick pipe is 44 cm. The level of water that 7 cm of that pipe can hold is
A) 798 $\text{cm}^3$
B) 308 $\text{cm}^3$
C) 792 $\text{cm}^3$
D) 795 $\text{cm}^3$

Answer 1

Hint:
We are given the circumference of the pipe. Using this, we can easily calculate the radius of the pipe. Then, we will subtract the thickness of the pipe from the radius to obtain the inner radius. Lastly, calculate the volume of the pipe using inner radius and given height.

Complete step by step solution:
We know that the circumference of a circle with radius $r$ is given by $2 \times \pi \times r$ .
The circumference of the given pipe is 44 cm. Then the radius can be calculated as
 $
  44 = 2 \times \pi \times r \\
   \Rightarrow 44 = 2 \times \dfrac{{22}}{7} \times r \\
   \Rightarrow r = 7 \\
 $ {Taking $\pi = \dfrac{{22}}{7}$ }
The radius of the given pipe is 7 cm.
According to the question, the pipe is 1 cm thick. So, the inner radius \[r'\] is,
\[
  r' = r - \text{thickness} \\
   \Rightarrow r' = 7 - 1 \\
   \Rightarrow r' = 6 \\
 \]
The inner radius that we calculated is 6 cm.
Now, to know the capacity of 7 cm of that pipe can hold, we must calculate the volume of pipe with height as 7cm. We already know, that the volume of a cylinder with height \[h\] and radius \[r'\] is given by :
\[
  V = \pi \times {(r')^2} \times h \\
   \Rightarrow V = \dfrac{{22}}{7} \times {6^2} \times 7 \\
   \Rightarrow V = 792 \\
 \] {Taking $\pi = \dfrac{{22}}{7}$ }

So, the volume of the pipe is 792 cm3 . Hence, we can say that the 7 cm of the given pipe can hold 792 cm3 of water.
The correct option is C.

Note:
Be careful by calculating the required areas or volumes, whenever the thickness of the container is mentioned. You must always subtract the thickness from the calculated dimensions in order to find the right area or volume.