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A cube shaped box has a side length of 15 inches and contains 27 identical cube shaped blocks. what is the surface area of all 27 blocks compared to the surface area of the box?

Sagot :

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

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