Question

a bar of soap is shaped like a right rectangular prism. the base is a rectangle that is 4 centimet by 2 centimeters. the height is 3 centimeters.
a second bar of soap is shaped like a square pyramid with the same volume as the first bar o soap. each side of the base of the pyramid is 2 centimeters in length.
what is the height of the pyramid?
36 cm
18 cm
3 cm
6 cm

Explanation:

Step1: Calculate the volume of the rectangular prism

The volume formula for a rectangular prism is \(V = l\times w\times h\). Here, \(l = 4\) cm, \(w=2\) cm, \(h = 3\) cm. So \(V=4\times2\times3=24\) \(cm^{3}\).

Step2: Use the volume formula for the square - pyramid

The volume formula for a square - pyramid is \(V=\frac{1}{3}s^{2}h_{p}\), where \(s\) is the side length of the base and \(h_{p}\) is the height of the pyramid. We know \(V = 24\) \(cm^{3}\) and \(s = 2\) cm. Substitute into the formula: \(24=\frac{1}{3}\times(2)^{2}\times h_{p}\).

Step3: Solve for \(h_{p}\)

First, simplify \(\frac{1}{3}\times(2)^{2}=\frac{4}{3}\). Then the equation becomes \(24=\frac{4}{3}h_{p}\). Multiply both sides by \(\frac{3}{4}\): \(h_{p}=24\times\frac{3}{4}=18\) cm.

Answer:

18 cm