Question

The formula of lateral surface area of the cylinder is ________.
(a). $A=2\pi rh$
(b). \[A=2\pi r\]
(c). \[A=\pi {{r}^{2}}\]
(d). \[A=2\pi {{r}^{2}}h\]

Answer 1

Hint: For a cylinder, the lateral surface area is the curved surface that connects the base and the top. We have to try to split the cylindrical shape into simpler shapes and then find the area of the curved surface.

Complete step-by-step answer:

We know that the lateral surface area of an object is defined as the area of all the sides of the object, excluding the area of its base and top. A cylinder has two faces, two curved edges where the curved wall meets the end circles, and a curved surface stretching between the two circular ends. Let us consider the figure below,

So, we can split the cylinder into two circles having diameter d and a rectangle having length as circumference of the circle given by $\pi d$ and width as h. So, here, we can clearly say that the lateral surface area would be the area of the rectangle portion alone.
So, we can write the lateral surface area formula as $\pi d\times h$. Now, we can write in terms of radius as \[\text{lateral surface area = }2\pi rh\].
Now, we have been asked the lateral surface area of the cylinder which is equal to \[2\pi rh\], where r is the radius and h is the height of the cylinder.
Therefore, the correct option of the above question is option A.

Note: The formula for calculating the lateral surface area is similar to the surface area formula, but since we are not including the top and base, we must remove that part of the formula. Also, be careful while choosing the correct option as you might get confused due to similar options. We have to find the formula of the lateral surface area of the cylinder, so it is obvious that the area must have its unit as sq. units. Using this, we can eliminate options B and D.