How can you use the formula for the volume of cylinder to remember the formula for the volume of a cone and the volume of a sphe
re?
2 answers:
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.
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Answer:
The time duration of the two pipes restricted flow before the flow became normal is 4.5 minutes
Step-by-step explanation:
The given information are;
The time duration for the volume, V, of the basin to be filled by one of the pipe, A, = 12 minutes
The time duration for the volume, V, of the basin to be filled by the other pipe, B, = 16 minutes
Therefore, the flow rate of pipe A = V/12
The flow rate of pipe B = V/16
Due to the restriction, we have;
The proportion of its carrying capacity the first pipe, A, carries = 7/8 of the carrying capacity
The proportion of its carrying capacity the second pipe, B, carries = 5/6 of the carrying capacity
Whereby the tank is filled 3 minutes after the restriction is removed, we have;
Simplifying gives;
2·t + 7 = 16
t = (16 - 7)/2 = 4.5 minutes
Therefore, it took 4.5 seconds of the restricted flow before the the flow of water in the two pipes became normal