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All Common Core: High School - Geometry Resources

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Flashcards: Geometric Methods to Solve Design Problems: CCSS.Math.Content.HSG-MG.A.3

Suppose you have a 12ft x 12ft area that you want to lay down tile for. Your tiles are 2ft x 2ft each. How many tiles do you need to perform this task?

64 tiles

144 tiles

36 tiles

4 tiles

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Flashcards: Geometric Methods to Solve Design Problems: CCSS.Math.Content.HSG-MG.A.3

Suppose you have a 12ft x 12ft area that you want to lay down tile for. Your tiles are 2ft x 2ft each. How many tiles do you need to perform this task?

Your answer:

64 tiles

Your answer:

144 tiles

Your answer:

4 tiles

Correct answer:

36 tiles

Explanation:

When it comes to word problems such as these, always begin by drawing an illustration. Below is a picture of our 12 x 12 area we need to fill with tiles and one 2 x 2 tile that we are going to use to fill this area.

There are two methods that we can use to solve this problem:

Method 1:

First we need to ask, how many tiles are needed to line the width of this 12 x 12 area. So if we have tiles that are 2 ft each we need to divide 12 by 2 to figure out how many tiles we need to line the width.

And so we need 6 tiles to line the width.

No we need to ask, how many tiles are needed to line the height of this 12 x 12 area. So if we have tiles that are 2 ft each we need to divide 12 by 2 to figure out how many tiles we need to line the height.

And so we need 6 tiles to line the width.

Now we need to find the total amount of tiles needed to fill the entire 12 x 12 space. We can solve for this just like we solve for area. We will multiply the amount of tiles across the width by the amount of tiles lining the height. This gives us an “area” in terms of the amount of tiles needed to fill the space.

And so we need 36 tiles to fill the space

Method 2:

We begin by finding the area of the entire 12 x 12 space. We use the fact that

And so our area of the entire space is . Now we need to find the area of each individual tile.

And so the area of each individual tile is . To find the total amount of tiles needed we need to find the amount of sections in the total area. To do this we divide:

Our units of cancel and we are left with 36 tiles.

Flashcards: Geometric Methods to Solve Design Problems: CCSS.Math.Content.HSG-MG.A.3

You have a barrel (cylinder) that is 1ft in radius and 3 ft in height. There was a thunderstorm the night before and you have found that the barrel is full of water. How much water is in the barrel? Round to the second decimal

156.01L

266.74L

9.42L

172.93L

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Flashcards: Geometric Methods to Solve Design Problems: CCSS.Math.Content.HSG-MG.A.3

Your answer:

156.01L

Your answer:

9.42L

Your answer:

172.93L

Correct answer:

266.74L

Explanation:

We must first recognize that this is a volume problem. There is a cylinder full of water and we must find the total volume of the cylinder in order to find the amount of water in the cylinder. We will use the formula for finding the volume of a cylinder, . is our radius and will be 1ft, is our height and will be 3ft.

But we cannot have represent volume. So we will use the conversion of cubic feet to liters. For every cubic foot there is 28.3168 liters.

Our units cancel and we are left with liters.

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All Common Core: High School - Geometry Resources

Flashcards: Geometric Methods to Solve Design Problems: CCSS.Math.Content.HSG-MG.A.3

Flashcards: Geometric Methods to Solve Design Problems: CCSS.Math.Content.HSG-MG.A.3

Flashcards: Geometric Methods to Solve Design Problems: CCSS.Math.Content.HSG-MG.A.3

Flashcards: Geometric Methods to Solve Design Problems: CCSS.Math.Content.HSG-MG.A.3

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