Math, asked by sahuh0488, 6 months ago

The water level in a cylinder raises by 16 cm when three spheres are dropped in it. If the ratio of the radii of the spheres is 1:2:3 and the radius of the cylinder is 6 cm, what is the volume of the smallest sphere in cm3?​

Answers

Answered by himanshujgupta199751
6

Step-by-step explanation:

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Answered by amitnrw
1

Given  : The water level in a cylinder raises by 16 cm when three spheres are dropped in it.

the ratio of the radii of the spheres is 1:2:3 and

the radius of the cylinder is 6 cm

To Find :  what is the volume of the smallest sphere in cm³ in π

Solution:

let say radius are  x , 2x and 3x  cm

Volume of sphere = (4/3)πr³

Volume of spheres are  (4/3)πx³  ,  (4/3)π(2x)³  and   (4/3)π(3x)³

=  (4/3)πx³  ,  (4/3)π8x³  and   (4/3)π27x³

Total  = (4/3)πx³ (1  + 8  + 27)

= (4/3)πx³ (36)

= 48πx³  cm³

Volume of cylinder = πr²h

r = 6 cm

level rise = 16 cm

Volume  of water raised =  π(6)² * 16  = 576π   cm³

48πx³   =  576π

=>  x³ = 12

volume of the smallest sphere  =   (4/3)πx³

=   (4/3) π12

=  16π  cm³

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