# The curved surface of a right circular cylinder of height 14cm is $88c{m^2}$. Find the diameter of the base of a cylinder.

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Hint: To solve this problem we have to use the formula of curved surface area of a cylinder, and we should also know the relation between radius and diameter which is basic but important.

Complete step-by-step answer:

Given the curved surface area of the circular cylinder =$88c{m^2}$.

Also given that height of (h) = 14cm

We know that curved surface area of circular cylinder = $2\pi rh$

Then we can say that

$ \Rightarrow 2\pi rh = 88$

$ \Rightarrow 2\pi r \times 14 = 88$ $[\because h = 14cm]$

$ \Rightarrow r = \dfrac{{88 \times 7}}{{28 \times 22}}$

$ \Rightarrow r = 1$

Therefore radius = 1cm

But here we have to find the diameter, we know that

d=2r

d=2(1) =2

Hence the diameter of the curved surface area of circular cylinder = 2cm

Note: In this problem they have given the value of the curved surface area of the circular cylinder where we have equated to its general formula, the formula includes the height which is already given in question. Now on substituting all required values we will get the radius of the circle but here we have to find the diameter. Since we know that diameter is twice the radius so now by using this relation we get the diameter of base of a cylinder which is our answer.

Complete step-by-step answer:

Given the curved surface area of the circular cylinder =$88c{m^2}$.

Also given that height of (h) = 14cm

We know that curved surface area of circular cylinder = $2\pi rh$

Then we can say that

$ \Rightarrow 2\pi rh = 88$

$ \Rightarrow 2\pi r \times 14 = 88$ $[\because h = 14cm]$

$ \Rightarrow r = \dfrac{{88 \times 7}}{{28 \times 22}}$

$ \Rightarrow r = 1$

Therefore radius = 1cm

But here we have to find the diameter, we know that

d=2r

d=2(1) =2

Hence the diameter of the curved surface area of circular cylinder = 2cm

Note: In this problem they have given the value of the curved surface area of the circular cylinder where we have equated to its general formula, the formula includes the height which is already given in question. Now on substituting all required values we will get the radius of the circle but here we have to find the diameter. Since we know that diameter is twice the radius so now by using this relation we get the diameter of base of a cylinder which is our answer.

Last updated date: 25th Sep 2023

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