Question

what is the volume of the card box?
a. $8\frac{3}{4}$ cu in
b. $6\frac{2}{3}$ cu in
c. $6\frac{1}{6}$ cu in
d. $5\frac{5}{6}$ cu in
picture not drawn to scale (with a diagram of a rectangular box labeled with dimensions $2\frac{1}{2}$ in, $3\frac{1}{2}$ in, $\frac{2}{3}$ in)

Explanation:

: $\frac{5}{2}×\frac{7}{2}=\frac{35}{4}$; $\frac{35}{4}×\frac{2}{3}=\frac{35}{6}$? No, wait: $2\frac{1}{2}=2.5$, $3\frac{1}{2}=3.5$, $\frac{2}{3}≈0.6667$; $2.5×3.5=8.75$, $8.75×0.6667≈5.8333=5\frac{5}{6}$? No, mistake: Wait the height is $\frac{2}{3}$? Wait no, original problem: Let's recheck: Volume of box is l×w×h. If l=2.5, w=3.5, h=2/3: 2.5×3.5=8.75, 8.75×2/3≈5.833=55/6? No, option D is 55/6. Wait but why? Wait 2.5=5/2, 3.5=7/2, 2/3: (5×7×2)/(2×2×3)=70/12=35/6≈5.833=55/6. Oh yes! 35/6=5 and 5/6. So answer is D? Wait no, wait the options: D is 55/6. Yes. So correction: Step3: Calculate $\frac{5}{2}×\frac{7}{2}×\frac{2}{3}=\frac{5×7×2}{2×2×3}=\frac{35}{6}=5\frac{5}{6}$. So answer is D.

Wait I made a mistake earlier. Let's redo:

Step1: Convert mixed numbers

$2\frac{1}{2}=\frac{5}{2}$, $3\frac{1}{2}=\frac{7}{2}$, height=$\frac{2}{3}$

Step2: Compute volume

Volume = $\frac{5}{2}×\frac{7}{2}×\frac{2}{3}$

Step3: Simplify fraction

Cancel 2: $\frac{5×7}{2×3}=\frac{35}{6}=5\frac{5}{6}$

Answer:

D. $5\frac{5}{6}$ cu in