Question

aaron bought a set of plastic ice cubes with a mixture of water and air inside.
what volume of water and air is inside each of the plastic ice cubes?
3,000 mm³ 1,500 mm³
4,500 mm³ 6,000 mm³

Explanation:

Step1: Recall the volume formula for a pyramid

The volume formula for a pyramid is \( V=\frac{1}{3}Bh \), where \( B \) is the base area and \( h \) is the height. The given shape is composed of two congruent pyramids.

Step2: Calculate the base area

The base is a rectangle with length \( l = 20\space mm \) and width \( w=15\space mm \). The area of the base \( B=l\times w=20\times15 = 300\space mm^{2}\).

Step3: Calculate the volume of one pyramid

The height of each pyramid \( h=\frac{30}{2}=15\space mm \). Using the formula \( V_{pyramid}=\frac{1}{3}Bh \), substitute \( B = 300\space mm^{2}\) and \( h = 15\space mm \). So \( V_{pyramid}=\frac{1}{3}\times300\times15=1500\space mm^{3}\).

Step4: Calculate the volume of the two - pyramid (ice - cube)

Since the ice - cube is made up of two such pyramids, \( V = 2\times V_{pyramid}\). Substitute \( V_{pyramid}=1500\space mm^{3}\), then \( V=2\times1500 = 3000\space mm^{3}\).

Answer:

\(3000\space mm^{3}\)