Question

the radius snd height of cylinder of the ratio 4:7 find the radius and height of the cylinder of its volume is 1188cm q also find tsa.

Answer 1

Since, the radius and height are in the ratio 4:7
let radius (r) be 4x and height (h) be 7x

Volume of a cylinder = πr²h
⇒ 1188 = π × (4x)² × 7x
⇒ 1188 = (22/7) × 16x² × 7x
⇒ 1188 = 22 × 16x² × x
⇒ 1188 = 352x³
⇒ x³ = 1188/352 = 27/8
⇒ x = ∛(27/8) = 3/2 = 1.5cm

Hence, radius of cylinder = 4x = 4×1.5 = 6cm
 & Height = 7x = 7×1.5 = 10.5 cm

TSA of Cylinder = 2πr(r+h)
                          = 2×(22/7)×6(6+10.5)
                          = 836.28 cm²
Hope it helps you!

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