Question

The radius and height of a cylinder are 80 cm and 20 cm respectively. The ratio of total surface area to the lateral surface area of cylinder is
A) 2 : 1
B) 3 : 1
C) 4 : 1
D) 5 : 1

Answer 1

Hint: In this question it is given that the radius and height of a cylinder are 80 cm and 20 cm respectively. So we have to find the ratio of total surface area to the lateral surface area of a cylinder.
So to find their ratio firstly we need to evaluate the total surface area (=curved surface area + area of top and bottom surface) and lateral surface area(= curved surface area).
Complete step-by-step solution:
Let us consider the radius of the given cylinder be r and height be h.
It is given that the radius r = 80 cm and height h = 20 cm.
So before solving we are going to draw the diagram-

Now we going to find the lateral surface area,
As we know that the formula of lateral surface area of a cylinder is,
L.S.A=$$2\pi rh$$
By using the above formula we can write the Lateral surface area, L.S.A=$$2\pi rh$$
          =$$2\pi \times 80\times 20$$ sq.cm
          =$$3200\pi$$.......................(1)
Now total surface area,
Formula for Total surface area of a cylinder is,
T.S.A=$$2\pi r\left( h+r\right)$$
So we can write for the given cylinder,
T.S.A=$$2\pi r\left( h+r\right) $$
        =$$2\pi \times 80\left( 20+80\right) $$
        =$$2\pi \times 80\times 100$$
        =$$16000\pi$$.......................(2)
Now the ratio of Total surface area and Lateral surface area is
$$\dfrac{T.S\cdot A}{L\cdot S\cdot A}$$
=$$\dfrac{16000\pi }{3200\pi }$$
= 5 : 1
So the correct option is D, i.e, 5 : 1
Note: Whenever you are asked to solve a problem which is related to shape or diagram then you must draw the figure, it will help you to understand and solve the problem easily. Here students may confuse between total surface area and lateral surface area.