Question

alicia has molds to make ice cubes in the shapes of two pyramids that have the same height but different bases. they are shown below. alicia says the volume of ice in shape 1, the rectangular pyramid, is three times the volume of ice in shape 2, the triangular pyramid. is alicia correct? use the formula below to determine the answer and use the drop - down menus to explain.
$v = \frac{1}{3}bh$
ice molds
(there are two pyramid figures: shape 1 is a rectangular pyramid with base length 4 cm, base width 3 cm, height 5 cm; shape 2 is a triangular pyramid with base triangle base 4 cm, base triangle height 3 cm, height 5 cm)
click the arrows to choose an answer from each menu.
the volume of ice in shape 1 is choose... cubic centimeters.
the volume of ice in shape 2 is choose... cubic centimeters.
shape 1 contains choose... ice as shape 2.
alicia choose... correct.

Explanation:

Step1: Calculate the volume of Shape 1

The base of Shape 1 is a rectangle. The area of the base \( B_1=3\times4 = 12\space cm^2\), and \(h = 5\space cm\). Using the formula \(V=\frac{1}{3}Bh\), we have \(V_1=\frac{1}{3}\times12\times5\).

$$V_1=\frac{1}{3}\times12\times5= 20\space cm^3$$

Step2: Calculate the volume of Shape 2

The base of Shape 2 is a triangle. The area of the base \(B_2=\frac{1}{2}\times4\times3=6\space cm^2\), and \(h = 5\space cm\). Using the formula \(V=\frac{1}{3}Bh\), we have \(V_2=\frac{1}{3}\times6\times5\).

$$V_2=\frac{1}{3}\times6\times5 = 10\space cm^3$$

Step3: Compare the volumes

We find the ratio \(\frac{V_1}{V_2}=\frac{20}{10}=2\). So Shape 1 contains twice as much ice as Shape 2.

Answer:

The volume of ice in shape 1 is \(20\) cubic centimeters.
The volume of ice in shape 2 is \(10\) cubic centimeters.
Shape 1 contains twice as much ice as shape 2.
Alicia is not correct.