Answer:
The side length of the blocks is 5 inches.
The total surface area of the 27 blocks is 4050 square inches.
This is 3 times the surface area of the box.
Step-by-step explanation:
Surface area of a cube
SA = 6s² (where s is the side length)
Given the side length of the box is 15 inches:
⇒ SA of box = 6 · 15² = 1350 in²
Surface Area of blocks with 3 inch side lengths:
⇒ SA = 6 · 3² = 54 in²
⇒ SA of 27 blocks = 27 · 54 = 1458 in²
Surface Area of blocks with 4 inch side lengths:
⇒ SA = 6 · 4² = 96 in²
⇒ SA of 27 blocks = 27 · 96 = 2592 in²
Surface Area of blocks with 5 inch side lengths:
⇒ SA = 6 · 5² = 150 in²
⇒ SA of 27 blocks = 27 · 150 = 4050 in²
Therefore, from the given answer options for the total surface area of the 27 blocks, the side length of the blocks must be 5 inches.
To calculate how many times the total surface area of the 27 blocks is to the surface area of the box:
[tex]\implies \dfrac{\textsf{SA of 27 blocks}}{\textsf{SA of box}}=\sf \dfrac{4050}{1350}=3[/tex]
Summary
The side length of the blocks is 5 inches.
The total surface area of the 27 blocks is 4050 square inches.
This is 3 times the surface area of the box.
