Question

if a cylinder and a cone are the same radius and height then how many cones full of milk can fill the cylinder answer with reason​

Answer 1

Given:

1. Radius of a Cylinder = Radius of a Cone = r units.
2. Height of the cylinder = Height of the cone = h units.

Find:

The number of cones of milk which can fill the cylinder completely.

Solution:

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

Volume of the cone =  $\frac{1}{3} \pi r^{2} h.$

Let the number of cones required to fill the cylinder be n.

Then n times the volume of 1 cone will be equal to the volume of the cylinder.

$n \times \frac{1}{3} \pi r^{2} h = \pi r^{2} h.\\\\\frac{n}{3} = \frac{\pi r^{2} h }{\pi r^{2} h }. \\\\\frac{n}{3} = 1.\\\\n = 3.$

Therefore, 3 cones of milk will be required to fill the cylinder completely.

Answer 2

$\bold{\underline{\underline{\huge{\tt{AnsWer:}}}}}$

$\bold{\large{\red{\sf{Number\:of\:cones\:required\:=\:3}}}}$

$\bold{\underline{\underline{\large{\tt{StEp\:by\:stEp\:explanation:}}}}}$

$\bold{\underline{\underline{\green{\tt{GiVeN:}}}}}$

• A cylinder and a cone of same radius.
• Height of the cylinder and cone is same

$\bold{\underline{\underline{\green{\tt{To\:FiNd:}}}}}$

• Number of cones of milk required to fill the cylinder

$\bold{\underline{\underline{\green{\tt{ SoLuTioN:}}}}}$

Let the number of cones required be x.

$\tt{Radius_{cone}\:=\:Radius_{cylinder}\:=\:r}$

$\tt{Height_{cone}\:=\:Heigt_{cylinder}\:=\:h}$

We know that,

• The volume of cone is ⅓ of the volume of cylinder.

The number of cones required will be x times the volume of cone equals the volume of cylinder.

$\longrightarrow$ $\tt{x\:\:\times\:Volume_{cone}\:=\:Volume_{cylinder}}$

Put the respective Formulaes,

$\longrightarrow$ $\tt{x\:\times\:{\dfrac{1}{3}\:\pi\:r^2\:h\:=\:\pi\:r^2\:h}}$

$\longrightarrow$ $\tt{x\:\times\:{\dfrac{1}{3}\:=\:{\dfrac{\pi\:r^2\:h}{\pi\:r^2\:h}}}}$

$\longrightarrow$ $\tt{x\:\times\:{\dfrac{1}{3}\:=\:1}}$

$\longrightarrow$ $\tt{\dfrac{1}{3}x\:=\:1}$

$\longrightarrow$ $\tt{x\:=\:1\:\times\:{\dfrac{3}{1}}}$

$\longrightarrow$ $\tt{x\:=\:3}$

$\tt{\therefore{3\:\:cones\:with\:radius\:and\:height\:same\:as\:that\:of\:cylinder\:is\:required}}$