Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • A sphere of diameter 12 cm, is dropped in a right circular cylinder vessel, partly filled with water. If the sphere is completely submerged in water, the water level in the cylinder vessel rises by   

A sphere of diameter 12 cm, is dropped in a right circular cylinder vessel, partly filled with water.

If the sphere is completely submerged in water, the water level in the cylinder vessel rises by   3 \frac{5}{9}   cm. Find the diameter  of the cylindrical vessel.

 

 

 

 

 
 
 
 
 

Answers (1)

Diameter of sphere = 12 cm 

radius of sphere = 12/2 = 6 cm 

increase in height in cyclinder vessel (H) = 3 \frac{5}{9} = 32/9

Let the radius of cylinder = R 

Rise in volume in water in cyclinder is equal to volume of the sphere 

\pi R^2 H = \frac{4}{3} \pi r^3 \\\\ R ^2 H = \frac{4}{3} r^3 \\\\ R^2 \times \frac{32}{9} = \frac{4}{3} \times 6 ^3 \\\\ R^2 = 4/3 \times 6 ^3 \times 9/32 \\\\ R^2 = \frac{4 \times 6 \times 6 \times 6 \times 9}{3 \times 32 } \\\\ R = \sqrt{\frac{4 \times 6 \times 6 \times 6 \times 9}{3 \times 32 } } = \sqrt {3 \times 3 \times 9} \\\\ R = 9 cm

Posted by

Ravindra Pindel

View full answer

Similar Questions

Latest Question