Question

The radius and height of a cylinder are in the ratio 5:7 and its volume is 550 $c{m^3}$. Find its radius.

Answer 1

Hint – In this question use the relation given between the height and radius of the rectangle along with the direct formula of the volume of the cylinder. Substitute h in terms of r in the formula for volume that is \[\pi {r^2}h\], to get the required radius.

Complete step-by-step answer:

Let the radius of the cylinder be r cm.
And the height of the cylinder be h cm as shown in figure.
Now it is given that the radius and the height are in the ratio 5 : 7.
$ \Rightarrow \dfrac{r}{h} = \dfrac{5}{7}$
$ \Rightarrow h = \dfrac{7}{5}r$..................... (1)
Now as we know that the volume (V) of the cylinder is $\pi {r^2}h$ cubic units where r and h are the radius and height of the cylinder respectively.
And it is given that the volume of the cylinder = 550 $cm^3$.
\[ \Rightarrow \pi {r^2}h = 550\]
Now from equation (1) substitute the value of h so we have,
\[ \Rightarrow \pi {r^2}\left( {\dfrac{{7r}}{5}} \right) = 550\]
Now simplify the above equation we have,
\[ \Rightarrow \dfrac{{22}}{7} \times \dfrac{7}{5}{r^3} = 550\]
\[ \Rightarrow {r^3} = \dfrac{{550}}{{\dfrac{{22}}{7} \times \dfrac{7}{5}}} = \dfrac{{550 \times 5}}{{22}} = 125 = {\left( 5 \right)^3}\] cm.
$ \Rightarrow r = 5$ cm.
So the radius of the cylinder is 5 cm.
So this is the required answer.

Note – A cylinder is one of the basic curved geometric shapes with the surface formed by the point at a fixed distance from a given line segment known as the axis of the cylinder and it is also the basic definition of the locus of the cylinder. It is advised to remember the direct basic formula for area, volume etc. for simple shapes like circle, cone, cylinder etc. as it helps solving problems of this kind.