A ball of diameter 20 cm fits exactly inside a cylindrical container, as shown below.

The maximum volume of liquid which can be poured into the cylindrical container when empty is ________ cm3.

[π=3.14]

Question

A ball of diameter 20 cm fits exactly inside a cylindrical container, as shown below.  

The maximum volume of liquid which can be poured into the cylindrical container when empty is ________ cm3. 

[π=3.14]

anonymous · Answer

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anonymous · Answer

If the diameter of the ball is 20 cm then the diameter of the cross section of the cylinder is also 20cm. Which means its radius is 10cm. This also means the height is 20cm. So the volume is:
$$V=\pi r^2 h=\pi (10)^2 (20)cm^3=2000 \pi cm^3$$

anonymous · Answer

Cylinder volume = base area * height.
Base are is same as ball's projection on xy plane which is a circle of radius 10. It's are is Pi*100. Multiply this by height of cylinder which is equal to 20cm, and you get Pi*2000 as the volume of it

anonymous · Answer

thank you guys!

mathstudent55 · Answer

If the ball has a diameter of 20 cm and fits exactly inside the cylinder, that means that the cylinder has a base of 20 cm diameter, and a height of 20 cm. You need to find the volume of that cylinder. The formula for the volume of a cylinder is
$$V = \pi r ^{2} h$$
where V = volume, r = radius of base, h = height
You have the diameter from which you can calculate the radius, and you have the height.