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A box has a length of 30 inches, a width of 40 inches, and a height of 120 inches. Can a cylindrical rod with a length of 342.9 centimeters fit in the box?
(A) yes
(B) no

A box has a length of $30$ inches, a width of $40$ inches, and a height of $120$ inches. Can a cylindrical rod with a length of $342$ . $9$ centimeters fit in the box? $\newline$ (A) yes $\newline$ (B) no

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Volume of cubes and rectangular prisms: word problems

Full solution

Q. A box has a length of

30

inches, a width of

40

inches, and a height of

120

inches. Can a cylindrical rod with a length of

342

.

9

centimeters fit in the box?

\newline

(A) yes

\newline

(B) no

Convert to inches: First, we need to convert the length of the cylindrical rod from centimeters to inches because the dimensions of the box are given in inches. There are $2.54$ centimeters in an inch. $\newline$ Calculation: $342.9 \, \text{cm} \times \left(\frac{1 \, \text{inch}}{2.54 \, \text{cm}}\right) = 135 \, \text{inches}$
Compare dimensions: Now we compare the length of the rod to the dimensions of the box to see if it can fit inside. The box has dimensions of $30$ inches by $40$ inches by $120$ inches. The rod is $135$ inches long.
Check length against height: The rod needs to fit within one of the dimensions of the box. Since the rod is $135$ inches long, it is longer than the length and width of the box, which are $30$ inches and $40$ inches, respectively. However, we need to check if it can fit within the height of the box, which is $120$ inches.
Conclusion: Comparing the rod's length to the height of the box, we see that $135$ inches is greater than $120$ inches. Therefore, the rod cannot fit within the box based on its height.

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