Question

Find the total surface area of a cylinder with diameter of base 7cm and height 40cm.
(a) 1016$c{{m}^{2}}$
(b) 880$c{{m}^{2}}$
(c) 1540$c{{m}^{2}}$
(d) 957$c{{m}^{2}}$

Answer 1

Hint: In this question, we have to find the total surface area of a cylinder. We are given its diameter and height. We have to use the formula $2\pi r\left( r+h \right)$ to find its surface area. We have to find the radius of the base using diameter. The relationship of radius and diameter is: diameter = 2$\times $ radius and radius is half of diameter.

Complete step by step solution:
Let’s solve the question and find its solution.

See the above figure, we are given diameter = 7cm and height = 40cm. First let’s find the radius. Diameter = 2$\times $ radius. So,
Radius = $\dfrac{diameter}{2}$
Radius = $\dfrac{7}{2}$cm
As we know that the formula for total surface area of the cylinder is: $2\pi r\left( r+h \right)$. Now, we will find the total surface area of the cylinder by using the given dimensions.
Radius r = $\dfrac{7}{2}$cm, height h = 40cm
$\Rightarrow 2\pi r\left( r+h \right)$
$\Rightarrow 2\times \dfrac{22}{7}\times \dfrac{7}{2}\left( \dfrac{7}{2}+40 \right)$
Solve the bracket first, take 2 as a denominator and then change the numerator:
$\begin{align}
  & \Rightarrow 2\times \dfrac{22}{7}\times \dfrac{7}{2}\left( \dfrac{7+80}{2} \right) \\
 & \Rightarrow 2\times \dfrac{22}{7}\times \dfrac{7}{2}\times \dfrac{87}{2} \\
\end{align}$
Now, next step is to reduce the terms:
$\Rightarrow 1\times \dfrac{11}{1}\times \dfrac{1}{1}\times \dfrac{87}{1}=957c{{m}^{2}}$
So the correct answer is option (d) i.e. $957c{{m}^{2}}$

Note: Students usually get confused with the formulae of cylinder. There are three formulae for cylinder: total surface area, curved surface area and volume. They all look similar so just have a note of them.
Total surface area: $2\pi r\left( r+h \right)$
Curved surface area: $2\pi rh$
Volume: $\pi {{r}^{2}}h$