Question

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

Answer 1

Hint: Firstly, we find the outer radius of the pipe from the circumference. Then we must find the inner radius of the pipe by subtracting the thickness from the outer radius of the pipe. Using the inner radius and given height, we can find the volume.

Complete step-by-step answer:
In the question it is given that the circumference of the pipe = 44 cm, and it’s thickness = 1 cm.
Now let us consider the radius of the pipe to be ‘r’$cm$.
We know that circumference is given by the equation ${{2 \times \pi \times r}}$.
From the question, we can formulate
${{2 \times \pi \times r = 44cm}}$
Now we substitute the value of \[\pi = \dfrac{{22}}{7}\], we get,
${{2 \times }}\dfrac{{{\text{22}}}}{{\text{7}}}{{ \times r = 44}}$
On further simplification we get,
${\text{r = }}\dfrac{{{{44}}}}{{{{2 \times 22}}}}{{ \times 7}}$
${\text{r = }}\dfrac{{{{44}}}}{{{{44}}}}{{ \times 7}}$
${\text{r = 7cm}}$
Therefore, we get radius of the pipe = 7 cm
We know that the thickness of the pipe is 1 cm,
Hence the inner radius of the pipe is found to be $7 - 1 = 6cm$
We have to find the volume of the water that 7 cm of the pipe can hold.
We know that Volume is given by the equation, ${{V = }}$${{\pi }}{{{r}}^{{2}}}{{h}}$, were ‘${{V}}$’ is the volume, ‘h‘ is the height (in this case level of water) and ‘r ‘ is the radius of the pipe.
From our previous calculations and given data, we have r = 6 cm and h = 7 cm.
Therefore, the volume of water in 7 cm pipe is
${{V = \pi \times }}{{{6}}^{{2}}}{{ \times 7}}$
Now we substitute the value of \[\pi = \dfrac{{22}}{7}\], we get,
${{V = }}\dfrac{{{{22}}}}{{{7}}}{{ \times 36 \times 7}}$
On further simplification we get,
${{V = 22 \times 36}}$
${\text{V = 792c}}{{{m}}^{\text{3}}}$
Thus the level of water that 7 cm of pipe can hold is ${\text{792c}}{{\text{m}}^{\text{3}}}$.
Hence the correct answer is option C

Note: We must visualize the pipe to get an idea about inner and outer radius. The thickness of the pipe must be reduced from outer radius to get the inner radius, else we will get the outer volume which will be greater than the required volume. The formulas of circumference of circle and volume of cylinder must be known.