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
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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