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

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 base - area of Shape 1

The base of Shape 1 is a rectangle with length $l = 4$ cm and width $w=3$ cm. The area of the base $B_1=l\times w = 4\times3=12$ $cm^2$. The height $h = 5$ cm. Using the volume formula $V=\frac{1}{3}Bh$, the volume of Shape 1, $V_1=\frac{1}{3}\times B_1\times h=\frac{1}{3}\times12\times5 = 20$ $cm^3$.

Step2: Calculate base - area of Shape 2

The base of Shape 2 is a triangle with base $b = 4$ cm and height $h_{base}=3$ cm. The area of the base $B_2=\frac{1}{2}\times b\times h_{base}=\frac{1}{2}\times4\times3 = 6$ $cm^2$. The height of the pyramid $h = 5$ cm. Using the volume formula $V=\frac{1}{3}Bh$, the volume of Shape 2, $V_2=\frac{1}{3}\times B_2\times h=\frac{1}{3}\times6\times5=10$ $cm^3$.

Step3: Compare the volumes

We find that $V_1 = 20$ $cm^3$ and $V_2 = 10$ $cm^3$. So, $V_1 = 2V_2$.

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.