Question

1. which expressions represent the volume of this rectangular prism in cubic units? select all that apply. a 3×4×6 b 24×12 c 12 + 12 + 12 d 24 + 24 + 24 e 18×4 (from unit 1, lesson 6) 3. a box of milk measures 4 cm by 10 cm by 30 cm. what is its volume in cubic centimeters? explain or show your reasoning. (from unit 1 lesson 7)

Explanation:

Step1: Recall volume formula

The volume formula for a rectangular - prism is $V = l\times w\times h$, where $l$ is length, $w$ is width and $h$ is height.

Step2: Solve for first prism

For the first rectangular prism with $l = 6$, $w = 3$ and $h = 4$, $V=6\times3\times4 = 72$.

• Option A: $3\times4\times6=72$, so it is correct.
• Option B: $24\times12 = 288

eq72$, so it is incorrect.

• Option C: $12 + 12+12=36

eq72$, so it is incorrect.

• Option D: $24 + 24+24 = 72$. Since $6\times4 = 24$ and $24\times3=72$, it is correct.
• Option E: $18\times4=72$. Since $6\times3 = 18$ and $18\times4 = 72$, it is correct.

Step3: Solve for second prism

For the box of milk with $l = 10$, $w = 4$ and $h = 30$, using the volume formula $V=l\times w\times h$, we have $V = 10\times4\times30$.
$V=10\times4\times30=1200$ cubic - centimeters.

Answer:

1. A. $3\times4\times6$, D. $24 + 24+24$, E. $18\times4$
2. The volume of the box of milk is 1200 cubic centimeters. The volume formula for a rectangular prism is $V = l\times w\times h$. Here, $l = 10$ cm, $w = 4$ cm and $h = 30$ cm. So $V=10\times4\times30 = 1200$ $cm^{3}$.