Question

The height of the circular cylinder is 10 cm and the radius of the base is 7 cm. Then find the difference between the total base area and the curved surface area?

Answer 1

Hint: The base of the cylinder is circle with a radius of 7 cm so the base area is the area of a circle which is equal to $\pi {{r}^{2}}$ where r is the radius of the circle and as cylinder contains two bases i.e. lower and upper so we have to multiply 2 by area of the circle to get the total base area. To find the curved surface area of the cylinder we are going to use the formula $2\pi rh$ where “r” and “h” is the radius and height of the cylinder respectively. Now, subtract the results of total base area and curved surface area.

Complete step-by-step answer:
In the below figure, we have drawn a right circular cylinder with radius 7 cm and height 10 cm.

We are asked to find the difference between the total base area and the curved surface area of the above cylinder. For that we are going to find the total base area and curved surface area.
As you can see from the above figure that base of the cylinder is a circle so the area of the base is the area of the circle which is equal to $\pi {{r}^{2}}$ where “r” is the radius of the circle. The radius of the circle is given as 7 cm so substituting the value of r in the formula of area of circle we get,
$\begin{align}
  & \pi {{r}^{2}} \\
 & =\pi {{\left( 7 \right)}^{2}} \\
\end{align}$
You can also see that two bases are given so total base area is multiplication of the above result by 2.
Total base area of the circular cylinder is equal to: $2\pi {{\left( 7 \right)}^{2}}$
Substituting $\pi $ as $\dfrac{22}{7}$ in the above expression we get,
$\begin{align}
  & 2\left( \dfrac{22}{7} \right){{\left( 7 \right)}^{2}} \\
 & =2\times 22\times 7 \\
 & =308c{{m}^{2}} \\
\end{align}$
The curved surface area of the cylinder is equal to: $2\pi rh$
In the above expression, “r” and “h” represents the radius and height of the cylinder respectively.
Substituting “r” as 7 cm and “h” as 10 cm in $2\pi rh$ we get,
$\begin{align}
  & 2\pi \left( 7 \right)\left( 10 \right) \\
 & =2\left( \dfrac{22}{7} \right)\left( 7 \right)\left( 10 \right) \\
 & =440c{{m}^{2}} \\
\end{align}$
The difference between total base area and the curved surface area of the cylinder is equal to:
$\begin{align}
  & \left( 440-308 \right)c{{m}^{2}} \\
 & =68c{{m}^{2}} \\
\end{align}$
Hence, the difference between the total base area and the curved surface area is $68c{{m}^{2}}$.

Note: Be careful while putting the values of “r” and “h” in the formula of areas. The units of “r” and “h” must be the same whether they are in cm or m. In this problem we are lucky that units of “r” and “h” are the same but this could not be the case in every problem. And always write the units of the area as we have shown above as $c{{m}^{2}}$. If you forget to write units in the exam it will cost you marks.