The closest approximation of the volume of the cone can be filled will be 4.431 cubic inches.
According to the given question.
The radius of cone is 1.25 inches.
Height of cone is 2.75 inches.
Diameter of ball = 0.5 inches
⇒ radiusof ball = 0.5/2 = 0.25 inches
Now,
The volume of cone
= (1/3)π(1.25)^2(2.75)
= 4.497 cubic inches
And
The volume of ball (sphere)
= (4/3)π(0.25)^3
= (4/3)(3.14)(0.015625)
= 0.19625/3
= 0.06541 cubic inches
Since, the ball is inside the cone.
Therefore,
The closest approximation of the volume of the cone can be filled
= volume of cone - volume of ball(sphere)
= 4.497 cubic inches - 0.06541 cubic inches
= 4.431 cubic inches
Hence, The closest approximation of the volume of the cone can be filled will be 4.431 cubic inches.
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