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Andrew [12]
3 years ago
6

Molly is painting a model house and needs to know how much paint she will need. She knows the surface area of the prism is 216 s

quare inches and the surface area of the pyramid is 84 square inches.
1. Which surface is shared by the two solids? What are the dimensions of this surface?

2. There is another surface that Molly does not need to paint, because it won’t show when she displays the model house. Describe that surface, and explain why it doesn't need to be painted.

3. To find the area Molly needs to paint, she should add the surface areas of both solids and subtract:

twice the area of the triangle
twice the area of the square
three times the area of the square
the area of the square

4. Find the area Molly needs to paint. Show your work, and be sure to include units with your answer.

Oh and here's an image to help you out

Mathematics
1 answer:
mrs_skeptik [129]3 years ago
5 0

Answer:

1. Base of pyramid; 6 in by 6 in

2. Base of prism; Its dimensions are also 6 in by 6 in, located at the bottom of the house and will not be seen, so it does not require painting.

3. twice the area of the square

4. Area = 228 inches squared

Step-by-step explanation:

For question 4, the area Molly needs to paint is found by adding all the surface areas and subtracting the 2 surfaces that will not be painted: base of pyramid and base of prism (outlined in red). According to the picture, these are both squares with 6 by 6 dimensions.

<h3>Step 1. Add all surface areas together</h3>

Prism: 6 surfaces

Surface area = 216 inches sq

  • Front = 6 x 6 = 36
  • Back = 6 x 6 = 36
  • Top = 6 x 6 = 36
  • Bottom (base) = 6 x 6 = 36
  • Side = 6 x 6 = 36
  • Other side = 6 x 6 = 36

Pyramid: 5 surfaces

Surface area = 84 inches sq

  • Bottom (base) = 6 x 6 = 36
  • Front triangle = (6 x 4)/2 = 12
  • Back = (6 x 4)/2 = 12
  • Side = (6 x 4)/2 = 12
  • Other side = (6 x 4)/2 = 12

TOTAL surface area: 216 inches + 84 inches = 300 inches sq

<h3>Step 2. Subtract surfaces that are NOT being painted</h3>

300 - base of pyramid - base of prism

300 - 2(36)

300 - 72

<u>228 inches sq</u>

Hope this helps!

Download pdf
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Answer:

<h2><em><u>11.2 - B to C</u></em></h2><h2><em><u>12 - B to A</u></em></h2><h2><em><u>8.8 - A to C</u></em></h2>

You have to multiply all the sides by 4.

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Hope this helped!

3 0
4 years ago
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3 years ago
Consider a prism ABCA'B'C' whose base is an equilateral triangle of side a. The projection of A' onto ABC is the centroid of ABC
Serggg [28]

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lsu is there to help you with this question

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
For which rational expression is 8 an excluded value ? check all that apply
denis23 [38]

<u>Answer:</u>

The correct answer options are C. \frac{x^2+5}{x-8} and D. \frac{x^2-x-56}{x^2-64}.

<u>Step-by-step explanation:</u>

The values which make the denominator equal to zero are called the excluded values.

Here, we can substitute 8 for x and check if it makes the denominator 0.

\frac{x-8}{x+8} = \frac{8-8}{8+8} =\frac{0}{16} =0

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\frac{x^2+5}{x-8} = \frac{8^2+5}{8-8} =\frac{69}{0}

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3 years ago
ack has a collection of 10 pairs of gloves in his wardrobe. Before a business trip, he has to pack his luggage, and he selects 8
Leto [7]

Answer:

\frac{{10 \choose 8}2^8}{{20 \choose 8}}\approx 0.091

Step-by-step explanation:

We can think of the 10 pairs of gloves as simply being gloves of different colors. Picking no matching pair is the same as picking no 2 gloves of the same color. To compute the probability of doing so, we can compute the number of ways to select 8 gloves from different colors, and divide that by the total number of ways to select 8 random gloves out of the 20 gloves.

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2nd step - We now have to choose which glove are we going to pick from each of the chosen colors. Either the left one or the right one. For the first chosen color we have 2 choices, for the second chosen color we have 2 choices, for the third chosen color we have 2 choices, and so on. Therefore the number of ways in which we could choose gloves from the chosen colors is 2^8

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{10 \choose 8 }2^8

Now, the total numer of ways in which we could choose 8 gloves out of the 20 gloves is simply {20 \choose 8}

So the probability of picking no mathing pair is

\frac{{10 \choose 8}2^8}{{20 \choose 8}}\approx 0.091

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