Determine the maximum number of reels of thread that will fit exactly into a rectangular box that is 120 mm…

Question

Determine the maximum number of reels of thread that will fit exactly into a rectangular box that is 120 mm wide and 195 mm long. Show ALL calculations.

ScanSolve AI Tutor · Accepted Answer

I'll solve Question 1 from the image, which asks to determine the maximum number of reels of thread that will fit into a rectangular box. This involves calculating how many reels fit along the length and width of the box.

Dimensions of the rectangular box:
- Length = $195 \text{ mm}$
- Width = $120 \text{ mm}$
Dimensions of a cylindrical reel of thread:
- Radius = $11.5 \text{ mm}$
- Diameter = $2 \times 11.5 \text{ mm} = 23 \text{ mm}$

Determine how many reels can fit along the length of the box.
$\text{Number of reels along length} = \frac{\text{Length of box}}{\text{Diameter of reel}} = \frac{195 \text{ mm}}{23 \text{ mm}}$ $\text{Number of reels along length} \approx 8.478$
Since only whole reels can fit, we take the floor of this value.
$\text{Number of reels along length} = 8$
Determine how many reels can fit along the width of the box.
$\text{Number of reels along width} = \frac{\text{Width of box}}{\text{Diameter of reel}} = \frac{120 \text{ mm}}{23 \text{ mm}}$ $\text{Number of reels along width} \approx 5.217$
Since only whole reels can fit, we take the floor of this value.
$\text{Number of reels along width} = 5$
Calculate the total maximum number of reels that can fit in the box.
$\text{Total number of reels} = (\text{Number of reels along length}) \times (\text{Number of reels along width})$ $\text{Total number of reels} = 8 \times 5$ $\text{Total number of reels} = 40$
The maximum number of reels of thread that will fit into the rectangular box is $\boxed{\text{40}}$ .

Determine the maximum number of reels of thread that will fit exactly into a rectangular box that is 120 mm wide and 195 mm long. Show ALL calculations.

Answer

Step-by-step solution

Determine how many reels can fit along the length of the box.

Determine how many reels can fit along the width of the box.

Calculate the total maximum number of reels that can fit in the box.

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