Question

The radius and height of a cylinder are in the ratio 2:3.If the volume of the cylinder is 1617 cu.cm, find its height

Answer 1

The radius and height of a cylinder are in the ratio 2:3.If the volume of the cylinder is 1617 cu.cm, find its height.

Answer :

Given : Volume of cylinder = 1617 cu.cm

Ratio of radius and height is 2 : 3.

To find : Height

Let r and h be the radius and height of the cylinder respectively.

Hence, their ratio is 2:3 ( Given )

r : h = 2 : 3 ( Given )

Let the common multiple be 'x'.

So, r = 2x

h = 3x ( To find )

We have to find h.

Volume of cylinder = 1617 cu. cm ( Given )

We know the formula of volume of the cylinder.

Volume of cylinder = π r^2 h.

Thus,

$\tt{ \pi r^2 h = 1617}$

$\tt{\frac{22}{7} \times (2x) {}^{2} \times 3x = 1617}$

$\tt {\frac{22}{7} \times 12x {}^{3} = 1617 }$

$\tt{ {x}^{3} = \frac{1617 \times 7}{22 \times 12}}$

$\tt{x {}^{3} = 42.875}$

$\tt{ x = \sqrt[3]{42.875} }$

$\tt{x = 3.5 \: cm}$

We got the value of x as 3.5.

Hence,

Height = 3x = 3 × 3.5

Height = 10.5 cm

Hence, Height of the cylinder is 10.5 cm.

Similarly, We can also find the radius of the cylinder as per the following.

Radius = 2x = 2 × 3.5

Radius = 7.0

Thus, Radius of cylinder is 7 cm.

Final Answer of your question is :

The height of the cylinder is 10.5 cm.

Answer 2

$\textbf{\huge{ANSWER:}}$

$\sf{Given:}$

Ratio of radius and height = 2:3

Volume of the cylinder = 1617 $cm^{3}$

$\sf{To\:find:}$

The height of the cylinder

$\sf{Solution:}$

⊙Let the radius and height be = 2x and 3x ( This is obtained according to the given ratio in the question )

We know that:

Volume of a cylinder = $\pi r^{2}h$

=》 Volume = 1617 $cm^{3}$

=》 $\pi (2x)^{2} (3x) = 1617$

=》 $4x^{2}(3x) = \frac{1617\times7}{22}$

=》 $12x^{3} = 514.5$

=》 $x^{3} = 42.875$

=》 $\tt{\boxed{x = 3.5 cm}}$

Radius of the cylinder = 2 × 3.5 = $\tt{\boxed{\boxed{7 cm}}}$

Height of the cylinder = 3 × 3.5 = $\tt{\boxed{\boxed{10.5 cm}}}$

What we did : We just found the values of the radius and the height according to the ratios given to us. Then, we put the obtained values in the Volume formula. Finally, we got our answer!✌