Question

Find the total surface areas of the following cylinders.

Answer 1

Hint: Here, in this given question, we must use the formula for the total surface area of a right circular cylinder that is the sum of the area of the bases and the curved surface area of the right circular cylinder that is $ 2\pi {{r}^{2}}+2\pi rh=2\pi r\left( r+h \right) $ , where r and h are the radius and height of the cylinders respectively, to find the required surface areas as the answers to this question.

Complete step-by-step answer:

In this given question, we are asked to find the total surface areas of the given cylinders that are:
The surface area of a right circular cylinder is the sum of the area of the bases and the curved surface area of the right circular cylinder that is $ 2\pi {{r}^{2}}+2\pi rh=2\pi r\left( r+h \right) $ ……………….. (1.1) , where r and h are the radius and height of the cylinders respectively.
Now, the radius and height of the first cylinder are 14cm and 8cm respectively.
So, its total surface area is
 $ 2\pi r\left( r+h \right)=2\times \dfrac{22}{7}\times 14\times \left( 14+8 \right)=1936c{{m}^{2}}.................(1.2) $
The radius and height of the second cylinder are 2m and 2m respectively.
So, its total surface area is
 $ 2\pi r\left( r+h \right)=2\times \dfrac{22}{7}\times 2\times \left( 2+2 \right)=50.28{{m}^{2}}........................(1.3) $
Therefore, we obtain our answers to the question as the total surface areas of the two cylinders equal to $ 1936c{{m}^{2}} $ and $ 50.28{{m}^{2}} $ respectively.

Note: In this sort of question, while calculating, the units need to be taken utmost care of. Like in this question, we calculated in centimeter square for the first cylinder but for the second cylinder we found the total surface area in meter square.