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If you were filling the cylinder up with water using a cone that has the same height and diameter, how many cones will it take to fill up the cylinder?

Sagot :

Answer:

It required 3 cones to fill up the cylinder with the same height and diameter.

Step-by-step explanation:

Let the radius of the cone and cylinder be r.

Let the height of the cone and cylinder be h.

As we know that  [tex]\text{Volume of cylinder}=\pi r^2h[/tex] ....(1)

[tex]\text{Volume of cone}=\frac{1}{3}\pi r^2h[/tex]

It can be observed that the volume of a cone is [tex]\frac{1}{3}[/tex]rd the volume of the cylinder. so, multiply the volume of the cone by 3.

[tex]3 \times \text{Volume of cone}=3 \times \frac{1}{3}\pi r^2h[/tex]

[tex]3 \times \text{Volume of cone}= \pi r^2h[/tex]

[tex]3 \times \text{Volume of cone}= \text{Volume of cylinder}[/tex] (From equation 1 )

Hence, It required 3 cones to fill up the cylinder with the same height and diameter.

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