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# Volume

What is the volume of a sphere of radius 5? If we make a cylinder two times taller, and its radius three times bigger, how many times larger would it become in volume?

# Volume - Cuboid

The swimming pool that Calvin goes to is a rectangular prism that has dimensions 20 meters long, 8 meters wide and 3 meters deep. What is the volume of water that the swimming pool contains (in $$\mbox{m}^3$$)?

In the above diagram, three identical containers $$A,$$ $$B$$ and $$C$$ contain water reaching heights $$a,$$ $$b$$ and $$c,$$ respectively. If the respective water volumes are $$12\text{ cm}^3,$$ $$20\text{ cm}^3$$ and $$28\text{ cm}^3,$$ what is the ratio $$a:b:c ?$$

The above diagram is a rectangular solid with width $$x,$$ length $$y$$ and height $$z.$$ If $$xy=10,$$ $$yz=20$$ and $$zx=8,$$ what is the volume of the rectangular solid?

Note: The above diagram is not drawn to scale.

In the above diagram, a small rectangular cuboid is cut off from a larger rectangular cuboid. If $$x=7,$$ $$y=4,$$ $$z=2$$ and $$w=3,$$ what is the volume of remaining body?

Note: The above diagram is not drawn to scale.

If $$a=9,$$ $$b=14$$ and $$c=9$$ in the above diagram, what is the volume of the rectangular cuboid?

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