Question

jamie just bought two boxes. the first box is square, with each side measuring 10 units, and is 4 units high. the second box is rectangular and has twice the volume of the square box. if the height of the second box is 5 units, and the width is 10 units, what is the length of the second box? a 10 units b 12 units c 16 units d 18 units click the button or type the letter next to your answer. question 10 of 15 39 minutes to go

Explanation:

Step1: Calculate volume of square - box

The volume formula for a rectangular - prism (square box here) is $V = s\times s\times h$, where $s$ is the side - length and $h$ is the height. For the square box, $s = 10$ units and $h = 4$ units. So $V_1=10\times10\times4 = 400$ cubic units.

Step2: Find volume of rectangular box

The volume of the second (rectangular) box is twice the volume of the square box. So $V_2 = 2\times V_1=2\times400 = 800$ cubic units.

Step3: Calculate length of rectangular box

The volume formula for a rectangular box is $V = l\times w\times h$. We know that for the rectangular box, $V = V_2 = 800$ cubic units, $w = 10$ units, and $h = 5$ units. We need to find $l$. Rearranging the formula $l=\frac{V}{w\times h}$. Substituting the values, we get $l=\frac{800}{10\times5}=\frac{800}{50}=16$ units.

Answer:

C. 16 units