Question

a conical vessel with radius 10 & h 15cm is completely filled with water .this water poured into a cylinder with radius 5cm find hieght of water in cylinder​

Answer 1

$\huge \bold{FOR \: CONE}$

$\bold{Radius \: r = 10 \: cm}$

$\bold{Height \: h = 15 \: cm}$

Given, that the conical vessel is filled with water so,

$\boxed{Volume \: of \: cone = Volume \: of \: water}$

$\huge \boxed{Volume \: of \: cone = \dfrac{1}{3} \times \pi \times {r}^{2} \times h}$

On placing values,

$\mathsf{Volume \: of \: cone = \dfrac{1}{3} \times \dfrac{22}{7} \times {10}^{2} \times 15}$

$\mathsf{Volume \: of \: cone = \dfrac{1}{3} \times \dfrac{22}{7} \times 10 \times 10 \times 15}$

$\huge \boxed{\mathsf{Volume \: of \: cone =1571.42 \: cm^{2}}}$

$\huge \bold{FOR \: CYLINDER }$

$\bold{Radius \: r = 5 \: cm}$

$\bold{Height \: h = ? }$

$\huge \boxed{Volume \: of \: cylinder = \pi \times {r}^{2} \times h}$

$\mathsf{Volume \: of \: cylinder = \dfrac{22}{7} \times 5 \times 5 \times h}$

$\huge \boxed{Volume \: of \: cylinder = 78.57 h}$

$\large\bold{ACCORDING \: TO Ä: QUESTION }$

The water of cone is transfered into a cylinder ,since the volume of water will remain same, therefore,

$\boxed{Volume \: of \: cylinder = Volume \: of \: water}$

Since,

$\boxed{Volume \: of \: cone = Volume \: of \: water}$

Therefore,

$\boxed{Volume \: of \: cone = Volume \: of \: cylinder}$

$\mathsf{1571.42 = 78.57 \times h}$

$\mathsf{\dfrac{1571.42}{78.57}= h}$

$\huge \boxed{HEIGHT = 20 \: cm}$