Respuesta :
The surface area of all 27 blocks compared to the surface area of the box is 3 times the surface area of the box.
What is a cube?
- A cube is a three-dimensional solid object with six square faces, facets, or sides, three of which meet at each vertex.
To find the total surface area of the 27 blocks:
A cube's surface area
- SA = 6s² (where s is the side length)
Given that the box's side length is 15 inches:
- SA of box = 6152 = 1350 in2
Surface Area of 3-inch side length blocks:
- ⇒ SA = 6 · 3² = 54 in²
- 27 blocks SA = 27 54 = 1458 in2
Surface Area of 4-inch side length blocks:
- ⇒ SA = 6 · 4² = 96 in²
- 27 96 = 2592 in2 SA of 27 blocks
Surface Area of 5-inch side length blocks:
- ⇒ SA = 6 · 5² = 150 in²
- 27 blocks SA = 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:
So,
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.
Therefore, the surface area of all 27 blocks compared to the surface area of the box is 3 times the surface area of the box.
Kow more about a cube here:
https://brainly.com/question/1972490
#SPJ4
