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1 answer:
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Answer: Choice A
The formula for the volume of a cone is 1/3 the volume of a cylinder. The volume of a sphere is 4/3 the volume of a cylinder, where the height of the cylinder is the same as the radius of the sphere
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Explanation:
As the first screenshot shows, the volume of a cone is 1/3 the volume of a sphere. The radius of each are the same. The height of each are the same as well.
The first screenshot also mentions "The volume of the half sphere is 2/3 the volume of the cylinder". The diagram shows the height of the cylinder (h) is equal to the radius of the half sphere. Based on this, the volume of a full sphere of radius r will be 4/3 times the volume of the cylinder with the same radius and height of 2r. You can think of having a spherical tennis ball inside a cylindrical can.
The first screenshot shows this when your teacher computed to get
Note how
The stuff in parenthesis represents the volume of a cylinder with radius r and height h = r. This is one way to see that
SphereVolume = (4/3)*(CylinderVolume)
where the height of the cylinder is as discussed above.
Answer:
14.13 cubic feet of lake water can fill the given balloon.
Step-by-step explanation:
concept used:
volume of sphere = 4/3
where r is the radius of sphere
we take = 3.14
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shape of balloon can be taken as spherical.
Amount water filled in the balloon will be equal to capacity of balloon which is equal to volume of spherical balloon.
Given radius of balloon = 1.5 feet
Thus, volume of balloon = 4/3 1.5^3 = 4/3*3.14*1.5^3
volume of balloon = 42.39/3 = 14.13 cubic feet
Thus, 14.13 cubic feet of lake water can fill the given balloon.