Question

A box has a length of 6 inches, a width of 8 inches, and a height of 24 inches. Can a cylindrical rod with the length of 63.5 centimeters fit in the box?

Answer 1

6 inches = 15.24 cm length
8 inches = 20.32 cm width
24 inches = 60.96 cm height

The diagonal along the side of the box = 20.32^2 + 60.96^2 = 4,129.024
square root (4,129.024) = 64.257 so the rod will fit diagonally.

Answer 2

Yes, the rod can fit in the box

Explanation:

First we have to convert the given size in inches to centimeters

1 inch = 2.54 centimeters

Length of the box = 6 × 2.54 = 15.24 cm

Width of the box = 8 × 2.54 = 20.32 cm

Height of the box = 24 × 2.54 = 60.96 cm

The longest diagonal in the box is the line between one of the top corners to the opposite bottom corner.

Calculate the length of the longest diagonal in the box:

`\sqrt{(20.32^(2)+60.96^(2) ) }`

=
`√(4129.024)`

= 64.257 cm.

Therefore, a cylindrical rod with the length of 63.5 centimeters can fit in the box.