Question

The radius and and height of a cylinder are in the ratio 4:7. and it's volume is
${1188cm}^{2}$
Find its radius​

Answer 1

Let the radius of the base and height of the cylinder be 4x and 7x respectively. Then Volume = 1188 cm³

$\implies\rm{ \pi r^{2} h=1188\:cm^3}$

$\implies\rm{ 22/7\times 16x^{2}\times 7x=1188\:cm^3}$

$\implies\rm{ 22\times 16x^{2}\times x=1188\:cm^3}$

$\implies\rm{ 352x^{2}\times x=1188\:cm^3}$

$\implies\rm{352x^{3}=1188\:cm^3}$

$\implies\rm{ x^{3}=1188/352\:cm^3}$

$\implies\rm{ x^{3}=3.375\:cm^3}$

$\implies\rm{ x=1.5\:cm}$

Therefore, Radius = 4x = 4 × 1.5 cm = 6 cm