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anonymous

  • one year ago

What is the surface area of the box if it is scaled up by a factor of 10?

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  1. anonymous
    • one year ago
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    The surface area of the box is 3246.54x (exponent 3).

  2. anonymous
    • one year ago
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    How do you figure this out?

  3. anonymous
    • one year ago
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    @Hero

  4. e.mccormick
    • one year ago
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    How can a surface area be cubic?

  5. anonymous
    • one year ago
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    i dont know lol i didnt do my work by hand

  6. anonymous
    • one year ago
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    1. List the dimensions of your box. Be sure to include the units (in, cm, ft., etc.). 2. Describe the shape of the cross section when the box is cut parallel to the base. 3. What is the surface area of the box? 4. What is the surface area of the box if it is scaled up by a factor of 10? 5. What is the volume of the box? 6. What is the volume of the box if it is scaled down by a factor of ½? This is what i got so far to step 2 .... Notebook (Rectangular Prism) Height – 10 ½ inches Width – 0.0984252 inches Length – 8 1/8 inches The shape has 4 parallel sides, it is a rectangular prism. The height would be 8 1/4 the width would be ¼ and the length would be 5 ½.

  7. e.mccormick
    • one year ago
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    Lines are single dimensional lengths, so go ip by linear values. Area is a square value, so they go up exponentially by 2. Volume is a cubic value, so it goes up exponentially by 3. 1 by 1 by 1 box to a 2 by 2 by 2 box to a 3 by 3 by 3 box... Lines: 1, 2, 3. Surface of one side: 1, 4, 9 Volume: 1, 8, 27 Notice a trend?

  8. anonymous
    • one year ago
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    Yes i do

  9. e.mccormick
    • one year ago
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    That is a narrow box!

  10. anonymous
    • one year ago
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    still a box sorta Its still a rectangular prism

  11. e.mccormick
    • one year ago
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    Yes. K, gonna check some math...

  12. anonymous
    • one year ago
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    ok

  13. e.mccormick
    • one year ago
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    How did you get that surface area?

  14. anonymous
    • one year ago
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    i did sa = 2 (wl + hl + hw)

  15. e.mccormick
    • one year ago
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    2(0.79970475 + 85.3125 + 1.0334646) = 174.2913387

  16. e.mccormick
    • one year ago
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    Now, if all the sides are up-scaled by 10, it becomes: sa = 2 (10w 10l + 10h 10l + 10h 10w) sa = 2 (100wl + 100hl + 100hw) sa = 2*100 (wl + hl + hw) So when you have the correct numbers, multiply by 100 to make something 10 times as long to see the new surface area. And 10^2=100... which is how it relates to what I was showing earlier. For the volume one, look at \(\left(\dfrac{1}{2}\right)^3\) for what to multiply by. Same principal applies. Half of each side, but cubed for area.

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