Question

The diagram shows an empty cylindrical container. Ana puts a solid cube of side length 8 cm into the container. She then pours 1.5 litres of water into the container. Will the water come over the top of the container? Explain your answer and show all your working.​

Answer 1

Cylinder

`\textsf{Volume of a cylinder}=\sf \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}`

Given:

• r = 6 cm

• h = 18 cm

`\begin{aligned}\implies \sf V &= \sf \pi (6)^2(18)\\& = \sf 648 \pi \: cm^3\end{aligned}`

Cube

`\textsf{Volume of a cube}=\sf x^3\quad\textsf{(where x is the side length)}`

Given:

• x = 8 cm

`\begin{aligned}\implies \sf V &= 8^3\\& = \sf 512 \: cm^3\end{aligned}`

Volume available to be filled with water

Volume of cylinder - volume of cube

= 684π - 512

= 1532.75204 cm³

1 litre = 1000 cm³

⇒ 1.5 litres = 1000 × 1.5 = 1500 cm³

As 1500 < 1532.75204, the volume of water poured into the container is smaller than the empty space available in the cylinder. Therefore, the water will not come over the top of the container.