Answer:
i. The company should use the cylindrical tubes.
ii. This is because the surface area of the cylindrical tubes, A' = 169.65 cm² is less than the surface area of the rectangular box, A = 202 cm²
Explanation:
i, Which packaging should the company choose?
The packaging that uses less material is the one with the least surface area. So, we find the surface area of each material.
For the rectangular box, the surface area, A = 2(lb + lh + bh) where l = length, b = breadth and h = height. Since each box is 8 cm by 3 cm by 7 cm,l = 8 cm, b = 3cm and h = 7cm.
So, ,A = 2(lb + lh + bh)
,A = 2( 8 cm × 3 cm + 8 cm × 7 cm + 3 cm × 7cm)
A = 2(24cm + 56 cm + 21cm)
A = 2(101 cm²)
A = 202 cm²
For the cylindrical tube, the surface area, A' = 2πr(r + h) where r = radius of cylinder and h = height of cylinder.
Since each cylinder has radius 3 cm and height 6 cm, r = 3cm and h = 6 cm.
So, A' = 2πr(r + h)
A' = 2π(3 cm)(3 cm + 6cm)
A' = (6π cm)(9 cm)
A' = 54π cm²
A' = 169.65 cm²
Since the surface area of the cylindrical tubes, A' = 169.65 cm² is less than the surface area of the rectangular box, A = 202 cm²
The company should use the cylindrical tubes.
ii. Justify your choice.
This is because the surface area of the cylindrical tubes, A' = 169.65 cm² is less than the surface area of the rectangular box, A = 202 cm²