Question

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A cone contains 100cm³ of sand. How many cones of sand can fill 2 cylinders of the same height and radius as the cone?​

Answer 1

$\huge \bf \underline{ \underline{Question}}$

A cone contains 100cm³ of sand. How many cones of sand can fill 2 cylinders of the same height and radius as the cone?

$\huge \bf \underline{ \underline{Answer}}$

Formula for volume of cylinder = πr²h

Formula for volume of cone = $\frac{1}{3} πr²h$

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Ratio of volumes of cylinder and cone

$\sfπr²h \: = \frac{1}{3} πr²h$

after canceling from both sides,

$\sf3:1$

It means that a cylinder can 3 times the volume of sand than cone.

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Therefore, 2 cylinders will hold

$= \sf2 \times 3 \times 100cm ^{3}$

$= \sf600cm^{3}$

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Two cylinders of same height and radius as the cone will hold 600cm³ of sand

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Answer 2

Formula for volume of cylinder = πr²h

Formula for volume of cone = $\frac{1}{3} πr²h$

Ratio of volumes of cylinder and cone

3 : 1

Therefore the 2 cylinders will hold

2 * 3 * 100cm³ = 600cm³ of sand