Question

Tanya's toy is deciding on dimensions for their boxes to store building blocks they want the box to have a volume of 48 inch^3 A. Find all the possible whole number dimensions for a box with a volume of 48 inch^3 (raise to 3) B. Which whole number dimensions would require the most wrapping paper to cover? C. Which whole number dimensions would require the least wrapping paper to cover?

Answer 1

(A) The possible dimensions are

1 inch × 2 inch × 24 inch                  

2 inch × 2 inch × 12 inch                  

3 inch × 2 inch × 8 inch                    

4 inch × 2 inch × 6 inch                    

4 inch × 4 inch × 3 inch                    

1 inch × 4 inch  × 12 inch                    

1 inch × 8 inch × 6 inch  

1 inch × 1 inch × 48 inch  

B) The dimensions with highest surface area will require the most wrapping paper which will be 1 inch × 1 inch × 48 inch  

C) The dimensions with least surface area will require least wrapping paper which will be 4 inch × 4 inch × 3 inch

Step-by-step explanation:

Volume of the box to store building blocks = 48 inch³

If the length, breadth and height of the box be l, b, h then

Volume of box = l × b × h

Surface area of the box = 2(lb + bh + hl)

If l, b, h are whole numbers then

Possible values of l × b × h and their surface areas are

1 × 2 × 24                   Surface area = 2(1 × 2 + 2 × 24 + 1 × 24) = 148 inch²

2 × 2 × 12                   Surface area = 2(2 × 2 + 2 × 12 + 12 × 2) = 104  inch²

3 × 2 × 8                     Surface area = 2(3 × 2 + 2 × 8 + 8 × 3) = 92 inch²

4 × 2 × 6                     Surface area = 2(4 × 2 + 2 × 6 + 6 × 4) = 88 inch²

4 × 4 × 3                     Surface area = 2(4 × 4 + 4 × 3 + 3 × 4) = 80 inch²

1 × 4 × 12                     Surface area = 2(1 × 4 + 4 × 12 + 12 × 1) = 128 inch²

1 × 8 × 6                      Surface area = 2(1 × 8 + 8 × 6 + 6 × 1) = 124 inch²

1 × 1 × 48                      Surface area = 2(1 × 1 + 1 × 48 + 48 × 1) = 194 inch²

The dimensions with highest surface area will require the most wrapping paper which will be 1 × 1 × 48  

The dimensions with least surface area will require least wrapping paper which will be 4 × 4 × 3

Hope this answer is helpful.

Know More:

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