Please explain how this is set up and how to work it. thanks
A rectangular box is 4cm wide, 4cm tall, and 10cm long. What is the diameter of the smallest circular opening through which the box will fit? Round to the nearest tenth of a centimeter.
We will certainly fit the box through the width and the height (4x4) instead of through the length (4x10).
The circular opening should have a diameter equal to the diagonal of the box (4x4).
Hint: use Pythagoras theorem to calculate the diagonal.
Thank you, but this did not help me.
Ouch. You do not know about the Pythagorean Theorem?
If not, look it up; you will be needing it a lot from now on. After that, come on back and we can clarify what you did not understand.
Thank you so much. You guys have been a lot of help to me in the past. I will study it more.
So would it be 4 squared plus 4 squared equals 32 then you take the square root of 32? Which is 5.65.
To find the diameter of the smallest circular opening through which the box will fit, we need to understand the dimensions of the box and how it fits inside a circular opening.
First, let's visualize the rectangular box. It has a width of 4cm, height of 4cm, and length of 10cm. It is important to note that when inserting the box through a circular opening, we need to consider the diagonal measure of the rectangular box. The diagonal represents the longest straight-line distance from one corner of the box to the opposite corner.
To find the diagonal of the rectangular box, we can use the Pythagorean theorem: a^2 + b^2 = c^2, where a and b are the sides of the rectangle, and c is the diagonal.
In this case, the width (a) and height (b) of the rectangle are both 4cm. Let's calculate the length of the diagonal (c):
a^2 + b^2 = c^2
4^2 + 4^2 = c^2
16 + 16 = c^2
32 = c^2
c ≈ √32 ≈ 5.6569 cm
So, the diagonal of the rectangular box is approximately 5.6569 cm.
Now, let's determine the diameter of the smallest circular opening through which the box will fit. The diameter is twice the radius of the circular opening.
Since the diagonal of the rectangular box represents the maximum distance it can fit through, we need to ensure that the diameter of the circular opening is at least equal to the diagonal.
Therefore, the diameter of the smallest circular opening would be approximately 2 * 5.6569 cm = 11.3138 cm.
To round to the nearest tenth of a centimeter, we round the diameter to one decimal place. Thus, the diameter of the smallest circular opening through which the box will fit is approximately 11.3 cm.