contestada

A heavy metal sphere with radius 10 cm is dropped into a right circular cylinder with base radius of 10 cm. If the original cylinder has water in it that is 40 cm​ high, how high is the water after the sphere is placed in​ it?

Respuesta :

Answer:

h = 53,3 cm is the new level of water in the cylinder

Step-by-step explanation:

V₁  = volume of the sphere       V₁  = (4/3)* π*r³

V₂  = volume of the cylinder     V₂ = π*r²*h

Then if the sphere is totally  inside  water,  the quantity of water sphere  shifts is equal to its  volume . That water will go up.

That shifts of water will occupy a new volume in the cylinder increasing the height of water according to the equation of the volume of the cylinder

That is ;

(4/3)*π*r³ = π*r²*h             h = the differece in height between rhe water level in the cilynder without the sphere and with the sphere

Then:  

(4/3)*r  = h

h  = 1.33 * 10        h = 13,3 cm

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