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: Find the area of the base

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

Step2: Recall the volume formula for a pyramid

The volume of a pyramid \(V=\frac{1}{3}Ah\), where \(A\) is the base - area and \(h\) is the height. The given figure is composed of two congruent pyramids with the same base.
Let the height of each pyramid be \(h_1 = h_2=30\) mm (since the total height from top - to - bottom through the base is composed of two equal - height parts from the two pyramids).
The volume of one pyramid \(V_1=\frac{1}{3}\times300\times30=3000\) \(mm^{3}\).
The volume of the two - pyramid (ice - cube) structure \(V = 2\times V_1\).
Since \(V_1=\frac{1}{3}\times300\times30\), then \(V=2\times\frac{1}{3}\times300\times30\).
Simplify \(V = 300\times20=6000\) \(mm^{3}\).

Answer:

\(6000\ mm^{3}\)