Surface Area and Volume of Similar Figures Unit 5, Lesson 10 Mrs. King.
-
Upload
brianna-reed -
Category
Documents
-
view
213 -
download
1
Transcript of Surface Area and Volume of Similar Figures Unit 5, Lesson 10 Mrs. King.
![Page 1: Surface Area and Volume of Similar Figures Unit 5, Lesson 10 Mrs. King.](https://reader035.fdocuments.net/reader035/viewer/2022072008/56649d755503460f94a561de/html5/thumbnails/1.jpg)
Surface Area and Volume of Similar FiguresUnit 5, Lesson 10Mrs. King
![Page 2: Surface Area and Volume of Similar Figures Unit 5, Lesson 10 Mrs. King.](https://reader035.fdocuments.net/reader035/viewer/2022072008/56649d755503460f94a561de/html5/thumbnails/2.jpg)
Volume of Similar Figures
![Page 3: Surface Area and Volume of Similar Figures Unit 5, Lesson 10 Mrs. King.](https://reader035.fdocuments.net/reader035/viewer/2022072008/56649d755503460f94a561de/html5/thumbnails/3.jpg)
What we discovered: If the similarity ratio of two similar solids
is a:b, then The ratio of corresponding surface areas
is a2:b2
The ratio of corresponding volumes is a3:b3
This applies to all similar solids, not just similar rectangular prisms.
![Page 4: Surface Area and Volume of Similar Figures Unit 5, Lesson 10 Mrs. King.](https://reader035.fdocuments.net/reader035/viewer/2022072008/56649d755503460f94a561de/html5/thumbnails/4.jpg)
Are the two solids similar? If so, give the similarity ratio.
Both solid figures have the same shape. Check that the ratios of the corresponding dimensions are equal.
The ratio of the radii is , and the ratio of the height is . 826
39
The cones are not similar because = . 826
39
/
![Page 5: Surface Area and Volume of Similar Figures Unit 5, Lesson 10 Mrs. King.](https://reader035.fdocuments.net/reader035/viewer/2022072008/56649d755503460f94a561de/html5/thumbnails/5.jpg)
Find the similarity ratio of two similar cylinders with surface
areas of 98π ft2 and 2π ft2.
Use the ratio of the surface areas to find the similarity ratio.
= 49 1
= 71
ab
Example 1:
= a2
b2
98 2
![Page 6: Surface Area and Volume of Similar Figures Unit 5, Lesson 10 Mrs. King.](https://reader035.fdocuments.net/reader035/viewer/2022072008/56649d755503460f94a561de/html5/thumbnails/6.jpg)
Example 2The surface are of two similar cylinders are 196 in2 and 324 in2. The volume of the smaller cylinder is 686in3. What is the volume of the larger cylinder?
First, find the similarity ratio of the sides! 196
324 REDUCE! 49
81 Find the square root 7 is the similarity ratio of the sides
9
![Page 7: Surface Area and Volume of Similar Figures Unit 5, Lesson 10 Mrs. King.](https://reader035.fdocuments.net/reader035/viewer/2022072008/56649d755503460f94a561de/html5/thumbnails/7.jpg)
Example 2The surface are of two similar cylinders are 196 in2 and 324 in2. The volume of the smaller cylinder is 686in3. What is the volume of the larger cylinder?
Now, create the similarity ratio of the sides into the similarity ratio of the volumes
73 = 343 93 729
Now, set up a new proportion 686 = 343
x 729 x = 1458
![Page 8: Surface Area and Volume of Similar Figures Unit 5, Lesson 10 Mrs. King.](https://reader035.fdocuments.net/reader035/viewer/2022072008/56649d755503460f94a561de/html5/thumbnails/8.jpg)
Example 3: The surface area of two similar solids are 160 m2 and 250 m2.
The volume of the larger one is 250 m3. What is the volume of the smaller one?
V = 128 m3
![Page 9: Surface Area and Volume of Similar Figures Unit 5, Lesson 10 Mrs. King.](https://reader035.fdocuments.net/reader035/viewer/2022072008/56649d755503460f94a561de/html5/thumbnails/9.jpg)
Two similar square pyramids have volumes of 48 cm3 and
162 cm3. The surface area of the larger pyramid is 135 cm2.
Find the surface area of the smaller pyramid.
Step 1: Use the ratio of the volumes to find the similarity ratio.
= 23
ab
Example:
= a3
b3 48 162
= 8 27
Step 2: Use the similarity ratio to find the surface area of the smaller pyramid.
S135
= 49
S = 60
= 22
32
![Page 10: Surface Area and Volume of Similar Figures Unit 5, Lesson 10 Mrs. King.](https://reader035.fdocuments.net/reader035/viewer/2022072008/56649d755503460f94a561de/html5/thumbnails/10.jpg)
A box of detergent shaped like a rectangular prism is 6 in. high and
holds 3.25 lb of detergent. How much detergent would a similar box
that is 8 in. tall hold? Round your answer to the nearest tenth.
The ratio of the heights is 6 : 8, or 3 : 4 in simplest terms.
Because the weights are proportional to the volumes, the ratio of the weights equals 33 : 43, or 27 : 64.
Example
= 3.25 x
2764
27x = 208
x 7.7037037
The box that is 8 in. tall would hold about 7.7 lb of detergent.