Answer:
339π in³
Explanation:
= π(5²)(15) - (4/3)π(3³)
= π(375 -36) = 339π . . . in³
The amount of water that can be filled in the considered cylinder given the 6-inch ball is still in it, is given by: Option 39π in³
Suppose that the radius of considered right circular cylinder be 'r' units.
And let its height be 'h' units.
Then, its volume is given as:
[tex]V = \pi r^2 h \: \rm unit^3[/tex]
Volume measures 3d space.
We will measure the amount of water that can be filled in the cylinder in terms of volume.
Given that:
Radius of cylinder = half of its diameter = 10/2 = 5 inches
Thus, we get:
Volume of the considered cylinder = [tex]V = \pi r^2 h = 5^2 \times 15 \times \pi = 375\pi \: \rm in^3[/tex]
Radius of the ball (assuming spherical in shape) = half of its diameter = 6/2 = 3 inches
Volume of that ball (assuming spherical in shape) = [tex]\dfrac{4}{3} \pi (3)^3 = 36\pi \: \rm in^3[/tex]
Space remaining in the cylinder for water to be filled (assuming water can't go inside the ball) = Space in the cylinder - space taken by the ball = volume of the cylinder - volume of the ball = [tex](375-36)\pi = 339\pi \: \rm in^3[/tex]
Thus, the amount of water that can be filled in the considered cylinder given the 6-inch ball is still in it, is given by: Option 39π in³
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