When converting from centimeters to inches, remember that 1 inch is 2.54 centimeters.
No, see solution.
Practice makes perfect
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 1in2.54cm.
342.9cm* 1in2.54cm
Now, we can evaluate the expression for the length of the rod.
The length of the cylindrical rod is 135 inches. Let's draw the box and the rod.
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.
Compare the length of the diagonal of the box and the length of the rod.
We will do it one step at a time.
Diagonal of the Base of the Box
Let's start by drawing the diagonal of the base of the box.
We can see that the diagonal divides the base of the box into two right triangles, with the diagonal as the hypotenuse. This means that we can use the Pythagorean Theorem to find the length of the diagonal of the base.
a^2+b^2=c^2
In the formula, a and b are the legs and c is the hypotenuse of a right triangle. Let's identify a, b, and c on the diagram.
We have that a= 30 inches and b= 40 inches. Let's substitute these values into the formula!
The diagonal of the base of the box is 50 inches long.
Diagonal of the Box
We know that the diagonal of the base of the box, the diagonal of the box, and the height of the triangle create a right triangle. Let's add this information to the diagram.
The diagonal of the box is the hypotenuse of the triangle. This means that we can once again use the Pythagorean Theorem to find the length. Let's identify the legs a and b, and the hypotenuse c on the diagram.
This time a is 50 inches and b is 120 inches. Let's substitute these values into the formula.
The diagonal of the box from a top corner to the opposite bottom corner is 130 inches long.
Compare the Length of the Diagonal of the Box and the Length of the Rod
Finally, we can compare the length of the diagonal of the box and the length of the rod. Let's do it!
130 < 135
The diagonal of the box is not as long as the length of the rod. This means that the rod will not fit in the box.
