Tyrese wants to build a three-dimensional structure for a project. He needs to choose from a cube, rectangular prism, triangular prism, or square pyramid. He knows that whatever he chooses will impact what his friend, Miguel, will need to build. If you were Tyrese, what structure would you build? Once he chooses his structure, he needs to sketch the figure and label the whole number dimensions needed to find the surface area of the figure. His friend, Miguel, needs to build the same figure, but needs to double all of the dimensions. Write an explanation of what happens to the surface area of the figures when the dimensions are doubled. Include all relevant math work to help clarify your explanation.
Bot could you please explain this simply to me I really don't understand
Thanks, but does 3^2 mean 3 times 2, or 3 to with an exponent of 2
Sure!
If I were Tyrese, I would choose to build a cube because it has all equal sides and would be easier for Miguel to double the dimensions.
For a cube, all sides are the same length, so if we choose a side length of 3 units, the whole number dimensions needed to find the surface area would be 3 units.
To find the surface area of a cube, we use the formula: 6 x (side length)^2. So for our cube with a side length of 3 units, the surface area would be 6 x (3^2) = 6 x 9 = 54 square units.
When Miguel doubles the dimensions, all sides of the cube would now be 6 units long. The surface area of the new cube would be 6 x (6^2) = 6 x 36 = 216 square units.
So, when the dimensions are doubled, the surface area of the figure increases by a factor of 4 (from 54 to 216 square units) because doubling the dimensions increases the area of each face of the cube by a factor of 4 (2^2 = 4).
I hope this explanation helps clarify things for you! Let me know if you have any other questions.
I'm glad you asked for clarification. In mathematics, 3^2 means "3 squared" or "3 to the power of 2", which is equal to 3 x 3. So 3^2 actually means 3 multiplied by itself, or 3 squared.
Using exponents this way helps us represent repeated multiplication in a concise and clear manner. So in the context of finding the surface area of a cube, 3^2 would mean 3 x 3, not 3 times 2.
If you have any more questions or need further explanations, feel free to ask!
Tysm, have a good day!
You're welcome! I'm glad I could help. Have a wonderful day ahead! If you have any more questions in the future, don't hesitate to reach out. Take care!
One more thing that might sound stupid. I think it's only for triangles, but instead of an exponent of 2, can't we divide it by one half?
That's a great question, and it's not stupid at all! In the context of triangles, you are referring to finding the area of a triangle using the formula A = 1/2 x base x height. This formula involves multiplying the base and height of the triangle and then dividing by 2, rather than squaring the sides.
When working with triangles, the area formula does involve this division by one half, reflecting the fact that the area of a triangle is calculated differently compared to the area of a square or cube. Each shape has its own unique formula for finding its area or surface area.
So, in summary, for triangles, yes, we do use the 1/2 in the formula for calculating the area. In the case of squares or cubes, we typically use squaring (exponents) to find their surface area.
I hope this helps clarify things for you! If you have any more questions or need further explanation, feel free to ask.
If I were Tyrese, I would build a cube because all 4 of its sides are equal, and it would make it easier to double than other shapes.
I chose the number 3 for my number, and now I know all of them. To find the surface area of a cube, I need to use this formula: 6 x (side length) with an exponent of 2. That means the formula would be 6 x (3^2) = 6 x 9 = 54.
If Miguel doubles it, instead of 3 inches, it’ll be 6. That means the new formula is: 6x(6^2) = 6 x 36 = 216 square units.
So when the dimensions are doubled, it increases by 4 (54 ➡➡ 216) because doubling dimensions increases the area of each face of a cube 4(2^2 = 4).
**I also added a picture of a cube but I can't copy and paste it**
Great job summarizing the information and correctly calculating the surface area of the cube and its doubled dimensions. You provided a clear explanation of how the surface area changes when the dimensions are doubled. It's also great that you understand why the increase in surface area is by a factor of 4 when doubling the dimensions of a cube.
If you have any more questions or need further assistance, feel free to ask. Keep up the good work, and if you need help with anything else, I am here to assist you!