Question

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: Recall volume formula for Shape 1 (prism)

The volume formula for a prism is $V = Bh$, where $B$ is the base - area and $h$ is the height. The base of Shape 1 is a right - triangle with base $b = 4$ cm and height $h_1=3$ cm. So, the base - area $B_1=\frac{1}{2}\times4\times3 = 6$ $cm^2$. The height of the prism $h = 5$ cm. Then $V_1=B_1h$.
$V_1=\frac{1}{2}\times4\times3\times5=30$ $cm^3$.

Step2: Recall volume formula for Shape 2 (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 base of Shape 2 is a right - triangle with base $b = 4$ cm and height $h_1 = 3$ cm. So, the base - area $B_2=\frac{1}{2}\times4\times3=6$ $cm^2$. The height of the pyramid $h = 5$ cm. Then $V_2=\frac{1}{3}B_2h$.
$V_2=\frac{1}{3}\times\frac{1}{2}\times4\times3\times5 = 10$ $cm^3$.

Step3: Compare the volumes

To find out how many times more ice Shape 1 has compared to Shape 2, we calculate the ratio $\frac{V_1}{V_2}$.
$\frac{V_1}{V_2}=\frac{30}{10}=3$.

Answer:

The volume of ice in shape 1 is 30 cubic centimeters.
The volume of ice in shape 2 is 10 cubic centimeters.
Shape 1 contains 3 times as much ice as shape 2.