Question

the radius and height of a cylinder are in the ratio 4: 7 and its volume is 118 8 cm cube find its radius

Answer 1

$let \: ratio \: be \: x \: thus \: ratio \: be \: 4x \div 7x \\ apply \: the \: formula \: of \: volume \: of \: cylinder \: ie. \: \pi \: r ^{2} h \: \\ we \: get \: x = 1.5 \\ so \: radius \: is \: 6cm$

Answer 2

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