Question

Jill is making a candle by pouring melted wax into a mold in the shape of a square pyramid. Each side of the base of the pyramid is 9 cm and the height of the pyramid is 10 cm. To get the wax for the candle, she melts cubes of wax that are each 4 cm by 4 cm by 4 cm. How many of the wax cubes will she need in order to make the candle? Show your work.

Answer 1

Step 1:

First, write the formula and find the volume of the pyramid of height 10cm and base sides 9cm.

`\text{Volume of a pyramid = }(1)/(3)\text{ base area }*\text{ height}`

Step 2:

Find the base area

`\begin{gathered} \text{The base is a square of length L = 9}cm \\ \text{Base area = Area of a square = L}^2 \\ \text{Base area = 9}^2 \\ \text{Base area = 81 }cm^2 \end{gathered}`

Step 3:

Find the volume of the pyramid.

`\begin{gathered} \text{Volume of the pyramid = }(1)/(3)*\text{ base area }*\text{ height} \\ \text{Volume of the pyramid = }(1)/(3)\text{ }*\text{ 81 }*\text{ 10} \\ \text{Volume of the pyramid = }(810)/(3)\text{ = 270 }cm^3 \end{gathered}`

Step 4:

Find the volume of a cube of a candle wax of sides 4cm by 4cm by 4cm.

`\begin{gathered} \text{Volume of a cube of side L = 4}cm\text{ is } \\ \text{Volume of a cube = 4 }*\text{ 4 }*\text{ 4} \\ \text{Volume of a cube = 64 }cm^3 \end{gathered}`

Step 5

To find the number of wax cubes she will need in order to make the candle

You will divide the volume of the pyramid by the volume of the cube.

The number of wax cubes she will need in order to make the candle

`\begin{gathered} =\text{ }(270)/(64) \\ =\text{ 4.21875} \\ =\text{ 5} \end{gathered}`

Final answer

5 wax cubes