Question

# The ratio between the curved surface area and the total surface area of a right circular cylinder is 1:2. Find the volume of the cylinder, if its total surface area is $616c{m^2}$.

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Hint-Using the formula of curved surface area of and total surface area of cylinder first let us find out the height and radius of the cylinder and using this let us find out the volume.

Curved surface area and total surface area are in the ratio of 1:2
So, if total surface area=$616c{m^2}$,Curved surface area=$\dfrac{{616}}{2} = 308c{m^2}$
Curved surface area = $2\pi rh = 308$
We know that total surface area of cylinder is given by $2\pi rh + 2\pi {r^2}$
Let's put $2\pi rh$ is nothing but equal to the curved surface area
So, we can write total surface area=308+$2\pi {r^2}$
So, we get $2\pi {r^2}$=616-308=308
$r = \sqrt {\dfrac{{308 \times 7}}{{2 \times 22}}} = 7cm$
From this we got the value of radius = r = 7cm
Now, let us find out the value of height
We have $2\pi rh = 308$, from this let us try to find out the value of h
So, we get $\begin{gathered} 2 \times \dfrac{{22}}{7} \times 7 \times h = 308 \\ \Rightarrow h = \dfrac{{308 \times 7}}{{2 \times 22 \times 7}} = 7cm \\ \end{gathered}$
So, now we have radius r=7cm, height h=7cm
Now, let us find out the volume
We know that the volume of the cylinder is given by the formula
$\begin{gathered} V = \pi {r^2}h \\ \Rightarrow V = \dfrac{{22}}{7} \times 7 \times 7 \times 7 = 1078cubic.cm \\ \end{gathered}$
So, from this we can write the volume of the cylinder =1078 cubic centimetres

Note: Make use of the appropriate formulas for curved surface area and total surface area of the cylinder when solving the problem. Also, make sure to represent the volume in cubic units.