We want to know if we can fit a cylindrical rod with a length of

342.9

centimeters in a box that has a length of

30

inches, a width of

40

inches, and a height of

120

inches. To compare the dimensions of the box and the length of the rod, they should have the same units. Let's start by converting

342.9

centimeters to inches using the conversion factor

\frac{1 in}{2 . 5 4 cm} .

342.9 cm \cdot \frac{1 in}{2 . 5 4 cm}

Now, we can evaluate the expression for the length of the rod.

342.9 cm \cdot \frac{1 in}{2 . 5 4 cm}

CrossCommonFac

Cross out common factors

342.9 cm \cdot \frac{1 in}{2 . 5 4 cm}

CancelCommonFac

Cancel out common factors

342.9 \cdot \frac{1 in}{2 . 5 4}

▼

Simplify

MovePartNumRight

$\frac{a \cdot b}{c} = \frac{a}{c} \cdot b$

342.9 \cdot \frac{1}{2 . 5 4} in

MoveLeftFacToNumOne

$a \cdot \frac{1}{b} = \frac{a}{b}$

\frac{3 4 2 . 9}{2 . 5 4} in

UseCalc

Use a calculator

135 in

The length of the cylindrical rod is

135

inches. Let's draw the box and the rod.

A box in the shape of rectangular right prism with the width of 30 inches, length of 40 inches and the height of 120 inches and a right cylinder with the height if 135 inches

Notice that the length of the rod,

135

inches, is longer than the longest side of the box,

120

inches. This means that the rod cannot fit in the box standing up. But we can also check if the rod will fit in the box diagonally. We can do this in three steps.

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