Question

The total surface area of the circular cylinder is \[1320c{m^2}\] and its radius is 10cm. find the height of the cylinder.

Answer 1

Hint: Given are the dimensions of the cylinder and the total surface area also. We just have to find the height of the cylinder. We will use the formula of the total surface area of the cylinder and just by putting the dimensions of the cylinder we can find the height of the cylinder.
Formula used:
Total surface area of the circular cylinder is given by,
\[2\pi r\left( {h + r} \right)\]

Complete step-by-step answer:
Given is the total surface area of the circular cylinder \[1320c{m^2}\]. So we can equate it as,
\[2\pi r\left( {h + r} \right) = 1320\]
We are also given the radius as 10cm. so we will take the value of r=10cm and that of \[\pi = 3.14\] then,
\[2 \times 3.14 \times 10 \times \left( {h + 10} \right) = 1320\]
Now on multiplying we get,
\[62.8 \times \left( {h + 10} \right) = 1320\]
Taking the numbers on right side we get,
\[h + 10 = \dfrac{{1320}}{{62.8}}\]
By multiplying the numerator and denominator by 10 on RHS we get,
\[h + 10 = \dfrac{{13200}}{{628}}\]
By dividing by 628 on RHS,
\[h + 10 = 21.01\]
\[h = 21.01 - 10\]
On subtracting we get,
\[h = 11.01cm\]
Thus this is the height of the circular cylinder \[h = 11.01cm\]
So, the correct answer is “ \[h = 11.01\;cm\]”.

Note: Note that total surface area of the cylinder includes area of the wall of the cylinder as well as the two circular top and bottom. They together form the total surface area. If the same question is asked for multiple choice and in the options if we see the pi terms is constant then don’t use its value. Keep it as it is.