moazzam07
  • moazzam07
Please help i dont know how to do this!!!!
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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moazzam07
  • moazzam07
1 Attachment
mathstudent55
  • mathstudent55
Are you home, so you have access to one of the objects the problem suggests? Do you have a ruler?
moazzam07
  • moazzam07
yes

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moazzam07
  • moazzam07
i asnwered number 1 but i dont understand the rest @mathstudent55
mathstudent55
  • mathstudent55
Ok. What kind of object are you using? A cereal box, something else?
moazzam07
  • moazzam07
a Box with 12 in Height, 12 in width, and 22 in length.
mathstudent55
  • mathstudent55
Ok. Great. Let me draw it below to help us answer the other questions.
mathstudent55
  • mathstudent55
Does that look like your box? |dw:1436729743433:dw|
moazzam07
  • moazzam07
yeah
mathstudent55
  • mathstudent55
Good. The answer to 1 is: 1. length = 22 in.; width = 12 in.; height = 12 in. Now let's look at part 2.
moazzam07
  • moazzam07
ok
mathstudent55
  • mathstudent55
When the box is in this position sitting on a surface (the floor or a table top), a base is the face of the box that sits on the surface. The top of the box is the other base. The two bases of the box are the bottom face and the top face.
moazzam07
  • moazzam07
so am i gonna list the surfaces?
mathstudent55
  • mathstudent55
Let's say we take a plane, and we let the plane go though the box. The plane must be parallel to the base, so it's a horizontal plane. I'll try to draw it for you.
moazzam07
  • moazzam07
ok
mathstudent55
  • mathstudent55
|dw:1436730068768:dw|
mathstudent55
  • mathstudent55
If you were to cut the box along that plane, and you look at teh box from the top, what shape is the box seen from the top?
moazzam07
  • moazzam07
a rectangle
mathstudent55
  • mathstudent55
|dw:1436730211052:dw|
mathstudent55
  • mathstudent55
Exactly.
mathstudent55
  • mathstudent55
Part 2. 2. a rectangle
mathstudent55
  • mathstudent55
Ok so far? Can we move on to part 3?
moazzam07
  • moazzam07
yes ok
mathstudent55
  • mathstudent55
3. we need the surface area of the box. We are now back to the original box, not the cut box from part 2. The box has 6 faces. Each face is a rectangle. We can find the area of the 6 rectangles and add them all up. That is the surface are a of the box.
mathstudent55
  • mathstudent55
|dw:1436730424100:dw|
mathstudent55
  • mathstudent55
We can take a short cut. Each two opposite faces have the same shape and area. We need to find the area of 3 different sides. Then we add them up and multiply by 2 since there are 2 faces of each size.
moazzam07
  • moazzam07
wait only 4 faces are rectangles 12 by 12 in is a square
mathstudent55
  • mathstudent55
There are 4 faces 12 in. by 22 in. There are 2 faces 12 in. by 12 in.
moazzam07
  • moazzam07
yeah
mathstudent55
  • mathstudent55
|dw:1436730608393:dw| The bottom, top, front and back faces measure 12 in. by 22 in. The right and left faces measure 12 in. by 12 in.
moazzam07
  • moazzam07
ok
mathstudent55
  • mathstudent55
\(Total ~surface ~area = 4 \times (22 ~in. \times 12 ~in.) + 2 \times (12 ~in. \times 12 ~in.)\)
mathstudent55
  • mathstudent55
What do you get for the total surface area?
moazzam07
  • moazzam07
1056+288= 1344in?
mathstudent55
  • mathstudent55
Great. That's what I got too.
moazzam07
  • moazzam07
yay
moazzam07
  • moazzam07
ok wat does it mean by scale factor of 10
mathstudent55
  • mathstudent55
Ok. Part 4. If every dimension of the box (length, width, and height) were to become 10 times larger, what wiould the new total surface area be?
mathstudent55
  • mathstudent55
A scale factor is a number you multiply something by to change its size. Here they ask you about a scale factor of 10. That means the length becomes 10 times larger, the width becomes 10 times larger, and the height becomes 10 times larger. Now the question is what will the new total surface area be?
moazzam07
  • moazzam07
3,786 In
mathstudent55
  • mathstudent55
How did you get that?
moazzam07
  • moazzam07
i mean 3,784
moazzam07
  • moazzam07
i added 10 to all the sides and remade the equation you made but this time with new numbers
moazzam07
  • moazzam07
am i wrong?
mathstudent55
  • mathstudent55
By the way, going back to part 3 for a second. The units must be units of area, so the total surface area is not 1344 in. It's 1344 in.^2. Square inches are units of area. Inches are units of length. Part 3 is an area, so the units are in.^2.
mathstudent55
  • mathstudent55
OK. Let me explain the scale factor again. A scale factor is a number you MULTIPLY by a given number. You don't add to a number. That means each dimension is MULTIPLIED by 10. You don't add 10 to each dimension. In general, the term "factor" in math relates to multiplication, not to addition.
moazzam07
  • moazzam07
am i wrong?
mathstudent55
  • mathstudent55
Yes, you are wrong because you added 10 to each dimension instead of multiplying each dimension by 10. Using the scale factor of 10 means each dimension now becomes 10 times larger. The length becomes 22 in. * 10 = 220 in. The width becomes 12 in. * 10 = 120 in. The height becomes 12 in. * 10 = 120 in.
mathstudent55
  • mathstudent55
You can now find the total surface are like we did before, but using the new 10-times larger dimensions, or you can take a short cut and do it much faster.
moazzam07
  • moazzam07
134400 in?
mathstudent55
  • mathstudent55
When the linear dimensions (length, width, and height) change by a scale factor of k, the surface area changes by a scale factor of k^2.
moazzam07
  • moazzam07
what is k
mathstudent55
  • mathstudent55
\(Total ~surface ~area = 4 \times (220 ~in. \times 120 ~in.) + 2 \times (120 ~in. \times 120 ~in.)\) \(= 105,600~in.^2 + 28,800~in.^2 = 134,400 ~in.^2\)
moazzam07
  • moazzam07
yay so i was right
mathstudent55
  • mathstudent55
k is the scale factor of the linear dimensions, length, width and height. In you case k is 10 since the linear dimensions went up by 10 times. That means the area goes up by k^2 times. Using 10 for k, the area goes up by 10^2 times = 100 times. The original area was 1,344 in^2. The new area is 1,344 in^2 * 100 = 134,400 in^2 As you can see, we get the same answer using the scale factor or using the area calculation.
mathstudent55
  • mathstudent55
Yes, you are correct. 4. 134,400 in^2
mathstudent55
  • mathstudent55
Now let's do part 5. How do you find the volume of a rectangular prism?
moazzam07
  • moazzam07
ok
moazzam07
  • moazzam07
how do i find the vouloum
mathstudent55
  • mathstudent55
It's like the volume of a cube. Multiply the length by the width by the height. \(V = LWH\)
mathstudent55
  • mathstudent55
In part 5 you need the volume of the original box. Just multiply the length by the width and then by the height. \(V = LWH = 22~in. \times 12~in. \times 12~in. \) The units of the volume are \(in.^3\), called cubic inches.
mathstudent55
  • mathstudent55
I have to go. Let's finish this before I go. Do you get an answer to part 5?
mathstudent55
  • mathstudent55
Instructions Search your home for a rectangular prism. Some examples are a cereal box, a CD case, or a coffee table. Measure your prism using appropriate units, such as inches, centimeters, or feet. Complete the following. Show all work for calculations. 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 $1/10$?
moazzam07
  • moazzam07
ok
moazzam07
  • moazzam07
i have got this so far
moazzam07
  • moazzam07
Instructions Search your home for a rectangular prism. Some examples are a cereal box, a CD case, or a coffee table. Measure your prism using appropriate units, such as inches, centimeters, or feet. Complete the following. Show all work for calculations. 1. List the dimensions of your box. Be sure to include the units (in, cm, ft, etc.) Answer to number 1: 12 in Height, 12 in width, and 22 in length. 2. Describe the shape of the cross section when the box is cut parallel to the base. Answer to number 2: A Rectangle 3. What is the surface area of the box? Answer to number 3: 1,344 in^2 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? Answer to number 5: 3,168 in 6. What is the volume of the box if it is scaled down by a factor of $1/10$?
mathstudent55
  • mathstudent55
Good. You did get part 5 correctly.
mathstudent55
  • mathstudent55
Now we need to do 6. When you apply a scale factor to a volume, you cube the scale factor. For example, if all sides change by a scale factor of 2, then the volume changes by a scale factor of 2^3. Since 2^3 = 2 * 2 * 2 = 8, the volume changes by 8 times.
moazzam07
  • moazzam07
yay
mathstudent55
  • mathstudent55
In your case, they tell you they want the scale factor to be 1/10 That means the length, width and height will all become 1/10 of what they were. Since the scale factor is 1/10, the volume becomes the cube of 1/10 What is \(\Large \left(\dfrac{1}{10} \right)^3 = \dfrac{1}{10} \times \dfrac{1}{10} \times \dfrac{1}{10} = \)
moazzam07
  • moazzam07
ok
moazzam07
  • moazzam07
1/100
moazzam07
  • moazzam07
1/1000
mathstudent55
  • mathstudent55
10 * 10 = 100 Here we have three 10's 10 * 10 * 10 = 1000
moazzam07
  • moazzam07
yes so 1/1000 rigth?
mathstudent55
  • mathstudent55
Correct. The volume becomes 1/1000 of what it was. Since the volume in part 5 was 3168 in.^3, now you divide that volume by 100 to find the answer to part 6.
moazzam07
  • moazzam07
31.68
mathstudent55
  • mathstudent55
In your answer above, make sure you use the correct units for part 5. A volume is in in.^3 (cubic inches), not plain in.
mathstudent55
  • mathstudent55
You divided by 100, not by 1000.
mathstudent55
  • mathstudent55
3168/1000 = ?
moazzam07
  • moazzam07
3.168
mathstudent55
  • mathstudent55
Great. Remember the units for parts 5 and 6 are in.^3
mathstudent55
  • mathstudent55
Now let's do it the other way. The original box was 22 in. by 12 in. by 12 in. The original volume is: 22 in. * 12 in. * 12 in. = 3168 in.^3 We now apply a scale factor of 1/10 to each side: The new cube now measures: 2.2 in. by 1.2 in. by 1.2 in. The new volume is: 2.2 in. * 1.2 in. * 1.2 in. = 3.168 in.^3 As you can see, the new volume comes out the same using both methods of calculation.
moazzam07
  • moazzam07
ok
moazzam07
  • moazzam07
do i put a ^3 for number 5 and 6
mathstudent55
  • mathstudent55
Yes, after "in." 5. 3168 in.^3 6. 3.168 in.^3
mathstudent55
  • mathstudent55
Also, parts 3 and 4 are areas, so the units are in.^2
mathstudent55
  • mathstudent55
That is it! Bye.
moazzam07
  • moazzam07
thanks bye
mathstudent55
  • mathstudent55
yw

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