Question

find the height of a cyclinder with a volume of 108π meter³ the radius of the cyclinder is twice the height.​

Answer 1

Answer:

volume of a cylinder = π r^2 h

108π = π (2h)^2 .h (since r=2h)

108π = π4h^3

h^3 = 108π/(π4) = 27

h = 3 m Ans

Answer 2

Given :

• Volume of cylinder = 108π m³
• Radius = 2× height

To find :

Height of cylinder

Formula used :

Volume of cylinder = π r²h

Solution :

Let , Height = h

Therefore Radius = 2h

$\sf \implies \: Volume \: = \: \pi \times {(2h)}^{2} \times h \\ \\ \sf \implies \: 108\pi \: {m}^{3} \: = \: \pi \times 4 {h}^{2} \times h \\ \\ \sf \implies \: \dfrac{108\pi \: {m}^{3} }{\pi} = 4 {h}^{3} \\ \\ \sf \implies \: \dfrac{108 \: {m}^{3} }{4} \: = {h}^{3} \\ \\ \sf \implies \: {h}^{3} = 27 \: {m}^{3} \\ \\ \sf \implies \:h \: = \sqrt[3]{27 \: {m}^{3} } \\ \\ \sf \implies \: \: h \: = \: \bold{ 3 \: m}$

ANSWER :

Height = 3m