Question

the radius and the height of a cylindrical are in the ratio 7:4 and its volume is 616 cm^3. find its radius.

Answer 1

$\text{Let r and h be the radius and height of the given cylinder respectively}$

$\textbf{Given:}$

$\text{Volume of the cylinder is 616 cubic cm and r:h=7:4}$

$\textbf{To find:}$

$\text{Radius of the cylinder}$

$\textbf{Solution:}$

$r:h=7:4$

$\text{Then,}$

$r=7k\;\text{and}\;h=4k$

$\text{Volume of the cylinder}=616\;cm^3$

$\implies\,\pi\,r^2\,h=616$

$\implies\,\dfrac{22}{7}{\times}(7k)^2{\times}4k=616$

$\implies\,\dfrac{1}{7}{\times}49\,k^2{\times}4k=28$

$\implies\,7\,k^2{\times}4k=28$

$\implies\,28\,k^3=28$

$\implies\,k^3=1$

$\implies\,k=1$

$\text{Radius}=7k=7(1)=7\;cm$

$\therefore\textbf{Radius of the cylinder is 7 cm}$

Find more:

Two circular cylinders of equal volume have their heights in the ratio 1 : 2. Ratio of their radii is

A. 1 :

B. : 1

C. 1: 2

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