Question

camille has two boxes with the dimensions shown. she wants to use the box with the greater volume to ship a gift to her friend.
write answers as mixed numbers.
box a volume = cubic inches
box b volume = cubic inches
which box should camille use? box
camille finds a third box, box c, that has a base with area of 22 square inches and a height of $10\frac{1}{2}$ inches. if camille wants to use the box with the greatest volume, should she use box c? type yes or no

Explanation:

Step1: Convert Box A to improper fractions

$7\frac{1}{2} = \frac{15}{2}$, $11\frac{1}{2} = \frac{23}{2}$

Step2: Calculate Box A volume

$\text{Volume}_A = \frac{15}{2} \times 2 \times \frac{23}{2} = 15 \times \frac{23}{2} = \frac{345}{2} = 172\frac{1}{2}$

Step3: Convert Box B to improper fractions

$2\frac{1}{4} = \frac{9}{4}$, $8\frac{1}{2} = \frac{17}{2}$

Step4: Calculate Box B volume

$\text{Volume}_B = 9 \times \frac{9}{4} \times \frac{17}{2} = \frac{81}{4} \times \frac{17}{2} = \frac{1377}{8} = 172\frac{1}{8}$

Step5: Compare Box A and B volumes

$172\frac{1}{2} > 172\frac{1}{8}$, so Box A is larger.

Step6: Convert Box C height to improper fraction

$10\frac{1}{2} = \frac{21}{2}$

Step7: Calculate Box C volume

$\text{Volume}_C = 22 \times \frac{21}{2} = 11 \times 21 = 231 = 231\frac{0}{1}$

Step8: Compare Box C to largest box

$231 > 172\frac{1}{2}$, so Box C is largest.

Answer:

Box A Volume = $172\frac{1}{2}$ cubic inches
Box B Volume = $172\frac{1}{8}$ cubic inches
Which box should Camille use? Box A
Should she use box C? YES