$4$ Two glass containers are shown. Both are right rectangular prisms. $\newline$ Container $1$ is filled with water and Container $2$ is empty. $\newline$ Container $1$ $\newline$ Container $2$ $\newline$ Amalia wants to pour all of the water from Container $1$ into Container $2$ . What must the height of Container $2$ be in order for it to hold the same amount of water as Container $1$ ? Round your answer to the nearest tenth. $\newline$ Type the numeric answer only, do not include units.

Full solution

4

Two glass containers are shown. Both are right rectangular prisms.

\newline

Container

1

is filled with water and Container

2

is empty.

\newline

Container

1

\newline

Container

2

\newline

Amalia wants to pour all of the water from Container

1

into Container

2

. What must the height of Container

2

be in order for it to hold the same amount of water as Container

1

? Round your answer to the nearest tenth.

\newline

Type the numeric answer only, do not include units.

Find Volume of Container $1$ : First, we need to find the volume of water in Container $1$ . Let's say the length is $l$ , the width is $w$ , and the height is $h_1$ . The volume $V_1$ is $l \times w \times h_1$ .
Find Height of Container $2$ : Now, we need to find the height of Container $2$ , which has the same length and width as Container $1$ , but a different height, $h_2$ . The volume $V_2$ for Container $2$ will be $l \times w \times h_2$ .
Set Volumes Equal: Since the volumes must be equal for Container $2$ to hold the same amount of water as Container $1$ , we set $V_1 = V_2$ . So, $l \times w \times h_1 = l \times w \times h_2$ .
Cancel Length and Width: We can cancel out the length and width since they are the same for both containers. This leaves us with $h_1 = h_2$ .