10-8 Areas and Volumes of Similar Solids. Similar solids have the same shape, and all their...
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Transcript of 10-8 Areas and Volumes of Similar Solids. Similar solids have the same shape, and all their...
![Page 1: 10-8 Areas and Volumes of Similar Solids. Similar solids have the same shape, and all their corresponding dimensions are proportional.](https://reader036.fdocuments.net/reader036/viewer/2022082819/56649f355503460f94c538cb/html5/thumbnails/1.jpg)
10-8 Areas and Volumes of Similar Solids
![Page 2: 10-8 Areas and Volumes of Similar Solids. Similar solids have the same shape, and all their corresponding dimensions are proportional.](https://reader036.fdocuments.net/reader036/viewer/2022082819/56649f355503460f94c538cb/html5/thumbnails/2.jpg)
Similar solids have the same shape, and all their corresponding dimensions are proportional.
![Page 3: 10-8 Areas and Volumes of Similar Solids. Similar solids have the same shape, and all their corresponding dimensions are proportional.](https://reader036.fdocuments.net/reader036/viewer/2022082819/56649f355503460f94c538cb/html5/thumbnails/3.jpg)
The ratio of corresponding linear dimensions of two similar solids is the similarity ratio.
Any two cubes are similar. Any two spheres are similar.
![Page 4: 10-8 Areas and Volumes of Similar Solids. Similar solids have the same shape, and all their corresponding dimensions are proportional.](https://reader036.fdocuments.net/reader036/viewer/2022082819/56649f355503460f94c538cb/html5/thumbnails/4.jpg)
Are the two solids similar?
![Page 5: 10-8 Areas and Volumes of Similar Solids. Similar solids have the same shape, and all their corresponding dimensions are proportional.](https://reader036.fdocuments.net/reader036/viewer/2022082819/56649f355503460f94c538cb/html5/thumbnails/5.jpg)
Are the two solids similar?
![Page 6: 10-8 Areas and Volumes of Similar Solids. Similar solids have the same shape, and all their corresponding dimensions are proportional.](https://reader036.fdocuments.net/reader036/viewer/2022082819/56649f355503460f94c538cb/html5/thumbnails/6.jpg)
Are the two solids similar?
![Page 7: 10-8 Areas and Volumes of Similar Solids. Similar solids have the same shape, and all their corresponding dimensions are proportional.](https://reader036.fdocuments.net/reader036/viewer/2022082819/56649f355503460f94c538cb/html5/thumbnails/7.jpg)
Areas and Volumes of Similar Solids
If the similarity ratio of two similar solids is a : b, then
1. The ratio of their corresponding areas is a2 : b2.
2. The ratio of their volumes is a3 : b3.
![Page 8: 10-8 Areas and Volumes of Similar Solids. Similar solids have the same shape, and all their corresponding dimensions are proportional.](https://reader036.fdocuments.net/reader036/viewer/2022082819/56649f355503460f94c538cb/html5/thumbnails/8.jpg)
The two solids are similar. Find the similarity ratio, the ratio of the areas, and the ratio of the volumes.
![Page 9: 10-8 Areas and Volumes of Similar Solids. Similar solids have the same shape, and all their corresponding dimensions are proportional.](https://reader036.fdocuments.net/reader036/viewer/2022082819/56649f355503460f94c538cb/html5/thumbnails/9.jpg)
The surface areas of two similar figures are given. The volume of the larger figure is given. Find the volume of the smaller figure.
S.A. = 25 cm2
S.A. = 36 cm2
V = 216 cm3
![Page 10: 10-8 Areas and Volumes of Similar Solids. Similar solids have the same shape, and all their corresponding dimensions are proportional.](https://reader036.fdocuments.net/reader036/viewer/2022082819/56649f355503460f94c538cb/html5/thumbnails/10.jpg)
The surface areas of two similar figures are given. The volume of the larger figure is given. Find the volume of the smaller figure.
S.A. = 16 in2
S.A. = 25 in.2
V = 500 in.3
![Page 11: 10-8 Areas and Volumes of Similar Solids. Similar solids have the same shape, and all their corresponding dimensions are proportional.](https://reader036.fdocuments.net/reader036/viewer/2022082819/56649f355503460f94c538cb/html5/thumbnails/11.jpg)
The volumes of two similar figures are given. The surface area of the smaller figure is given. Find the surface area of the larger figure.
V = 8 ft3
V = 125 ft3
S.A. = 4 ft2
![Page 12: 10-8 Areas and Volumes of Similar Solids. Similar solids have the same shape, and all their corresponding dimensions are proportional.](https://reader036.fdocuments.net/reader036/viewer/2022082819/56649f355503460f94c538cb/html5/thumbnails/12.jpg)
The volumes of two similar figures are given. The surface area of the smaller figure is given. Find the surface area of the larger figure.
V = 40 m3
V = 135 m3
S.A. = 40 m2
![Page 13: 10-8 Areas and Volumes of Similar Solids. Similar solids have the same shape, and all their corresponding dimensions are proportional.](https://reader036.fdocuments.net/reader036/viewer/2022082819/56649f355503460f94c538cb/html5/thumbnails/13.jpg)
Homework:
p. 5681 - 16