Question

The radius and height of a cylinder are in the ratio 2:3. If the volume of a cylinder is 1617cm cube.Find its radius and height​

Answer 1

Answer

Let the radius be , " 2x "

Height be , " 3x "

Volume of Cylinder = πr²h

Given , Volume of cylinder = 1617 cm³

$\bf :\to \pi r^2h=1617\\\\:\to \rm \pi (2x)^2(3x)=1617\\\\:\to \rm 12x^3\ \pi=1617\\\\:\to \rm x^3=42.875\\\\:\to \rm x=3.5$

So , Radius , 2x = 7 cm $\orange{\bigstar}$

Height , 3x = 10.5 cm $\green{\bigstar}$

Answer 2

Answer

→ Radius = 7 cm

→ Height = 10.5 cm

$\orange{\bigstar}$ Given $\green{\bigstar}$

Radius and height of a cylinder are in the ration 2 : 3

Volume of a cylinder is 1617 cm³

$\orange{\bigstar}$ To Find $\green{\bigstar}$

Radius of a cylinder

Volume of a cylinder

$\orange{\bigstar}$ Key Points $\green{\bigstar}$

Volume of a cylinder = πr²h

where ,

→ r denotes radius of a cylinder

→ h denotes height of a cylinder

→ π denotes a constant having value ²²/₇

$\orange{\bigstar}$ Solution $\green{\bigstar}$

Let the radius of the cylinder be 2x

and Height be 3x

Given ,

Volume of the cylinder = 1617 cm³

$\to \rm \pi r^2h=1617\\\\\to \rm \pi (2x)^2(3x)=1617\\\\\to \rm 12\pi x^3=1617\\\\ \to \rm x^3=\dfrac{1617}{12\pi}=\dfrac{539}{4\pi}\\\\\to \rm x^3=42.875\\\\\to \rm x=3.5\\\\\to \rm\ \orange{\bigstar}\ \; \blue{x=\dfrac{7}{2}}\ \; \green{\bigstar}$

So , Radius = 7 cm [ ∵ r = 2x ]

Height = $\rm \dfrac{21}{2}=10.5\ cm$ [ ∵ h = 3x ]