Answered

Welcome to Westonci.ca, where curiosity meets expertise. Ask any question and receive fast, accurate answers from our knowledgeable community. Explore thousands of questions and answers from knowledgeable experts in various fields on our Q&A platform. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.

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

#SPJ4

Thank you for visiting our platform. We hope you found the answers you were looking for. Come back anytime you need more information. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.