Question

(34)th of a cylindrical vessel of height 6 cm is full of water. When the water in the cylinder is emptied into a hemispherical vessel of radius 6 cm, it fills half the volume of this vessel. Find the radius of the cylindrical vessel. ​

Answer 1

Answer:

equal to the volume of water in the cylindrical vessel.

Volume of a Cylinder of Radius "R" and height "h" =πR

2

h

Volume of a cone =

3

1

πr

2

h, where r is the radius of the base of the cone and h is the height.

Hence,

7

22

×10×10×h=

3

1

×

7

22

×5

2

×24

⇒h=2 cm

Hence, height of water in the cylindrical vessel is 2 cm.

Answer 2

Radius of the cylindrical vessel is 12cm

Given,

Cylindrical vessel height,h= 6cm

Radius of Hemispherical vessel,r'= 6cm

To calculate,

Radius of Cylindrical vessel say "r"

Volume of Cylindrical vessel= 2πrh

     =2×$\frac{22}{7}$×r×6

     = $\frac{264}{7}$r                                                       (say, equation 1)

Volume of hemispherical vessel= $\frac{2}{3}$$\pi r'^{3}$

    = $\frac{2}{3}$×$\frac{22}{7}$×$6^{3}$

    = 452.57$cm^{3}$                                            (say, equation 2)

As the volume of water remains same even when the shape of the containers change.

Hence, by equating both the equations we get,

  ⇒ $\frac{264}{7}$r = 452.57

  ⇒ r= $\frac{452.57*7}{264}$

  ⇒ r= 12cm

/for more such questions on Volume: https://brainly.in/question/571343

#SPJ3