A mineral contains a cubic and spherical cavity. The length of the side of the cube is the same as the
diameter of the sphere. If the cubic cavity is half filled with a liquid and the spherical cavity is completely
filled with liquid, what is the approximate ratio of the volume of the liquid in the cubic cavity to that in the
spherical cavity?
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3
Answer:
21:22 approx 1:1
Step-by-step explanation:
Let say Length of side of cube = x
then Diameter of sphere = x
Radius of sphere = x/2
Volume of cube = x³
Half filled so volume of liquid = x³/2
Volume of sphere = (4/3)π(x/2)³ = πx³/6
fully filled Volume of liquid = πx³/6
volume of the liquid in the cubic cavity /Volume of liquid in spherical cavity = (x³/2)/(πx³/6)
= 3/π
= 3/(22/7) (π = 22/7)
= (3 * 7) /22
= 21/22
21:22 is the ratio
Approx 1:1
vaishali2412:
but options are these a) 2:1 b) 1:1 c) 1:2 d) 1:4 which is correct and how
I made a mistake from this step (4/3)π(x/2)³ = 3πx³/2. Actually it should have been πx³/6 so answer would be 63:66. Which is approximately 1:1
I will correct the solution tomorrow
63:66 = 21:22 approx 1:1
tq
Welcome solution corrected
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