Answer
Number of labels that the company can make from one sheet = 7
Step-by-step explanation
We are told the eraser casing covers the whole eraser.
So, if we calculate the total surface area of one eraser box, we can obtain how many eraser boxes of this calculated surface area can be obtained from the given area of sheet.
Total area of the sheet
= (Number of eraser boxes that can be made from this sheet) × (Area of one eraser box)
Total area of the sheet = L × W = 15 × 21 = 315 square inches
Number of eraser boxes that can be made from this sheet = n = ?
Area of one eraser box = Total surface area of a cuboid
= 2 (LB + LH + BH)
For the eraser box,
L = 4 inches
B = 3 inches
H = 1.5 inches
Area of one eraser box = Total surface area of a cuboid
= 2 (LB + LH + BH)
= 2 [(4 × 3) + (4 × 1.5) + (3 × 1.5)]
= 2 [12 + 6 + 4.5)
= 2 (22.5)
= 45 square inches.
Total area of the sheet
= (Number of eraser boxes that can be made from this sheet) × (Area of one eraser box)
315 = n × 45
315 = 45n
We can rewrite this as
45n = 315
Divide both sides by 45
(45n/45) = (315/45)
n = 7 eraser boxes
Hope this Helps!!!