Question

name:volume of rectangular prismszoe paints small wooden boxes and places her gemstones in them. the table below shows the dimensions of each box. find the volume of each box.| box color | length | width | height | volume || ---- | ---- | ---- | ---- | ---- || green box | 9 cm | 6 cm | 2 cm | $108 cm^3$ || yellow box | 2 cm | 4 cm | 7 cm | $56 cm^3$ || orange box | 3 cm | 5 cm | 5 cm | $75 cm^3$ || brown box | 8 cm | 4 cm | 3 cm | $168 cm^3$ || red box | 4 cm | 6 cm | 7 cm | $96 cm^3$ || blue box | 2 cm | 5 cm | 8 cm | $80 cm^3$ |color each box the correct color.a. volume = $168 cm^3$b. volume = $96 cm^3$c. volume = $80 cm^3$d. volume = $75 cm^3$e. volume = $108 cm^3$f. volume = $56 cm^3$g. zoe also has a black box. it is 14 cm tall, 3 cm deep, and 2 cm wide. what is the volume of this box?$104 cm^3$

Explanation:

The volume of a rectangular prism is calculated using the formula $V = l \times w \times h$, where $l$ = length, $w$ = width, $h$ = height.

Step1: Calculate green box volume

$V = 9 \times 6 \times 2 = 108$ $\text{cm}^3$

Step2: Calculate yellow box volume

$V = 2 \times 4 \times 7 = 56$ $\text{cm}^3$

Step3: Calculate orange box volume

$V = 3 \times 5 \times 5 = 75$ $\text{cm}^3$

Step4: Calculate brown box volume

$V = 8 \times 4 \times 3 = 96$ $\text{cm}^3$

Step5: Calculate red box volume

$V = 4 \times 6 \times 7 = 168$ $\text{cm}^3$

Step6: Calculate blue box volume

$V = 2 \times 5 \times 8 = 80$ $\text{cm}^3$

Step7: Match volumes to diagrams

a. Volume = 168 $\text{cm}^3$ → red box
b. Volume = 96 $\text{cm}^3$ → brown box
c. Volume = 80 $\text{cm}^3$ → blue box
d. Volume = 75 $\text{cm}^3$ → orange box
e. Volume = 108 $\text{cm}^3$ → green box
f. Volume = 56 $\text{cm}^3$ → yellow box

Step8: Calculate black box volume

$V = 3 \times 2 \times 14 = 84$ $\text{cm}^3$

Answer:

Table Volumes:

• green box: $108 \text{ cm}^3$
• yellow box: $56 \text{ cm}^3$
• orange box: $75 \text{ cm}^3$
• brown box: $96 \text{ cm}^3$
• red box: $168 \text{ cm}^3$
• blue box: $80 \text{ cm}^3$

Diagram Matches:

a. red box
b. brown box
c. blue box
d. orange box
e. green box
f. yellow box

Black Box Volume:

$84 \text{ cm}^3$