Which the following could represent the scale factor of the smaller figure to the larger figure?
Two pyramids are shown and one is larger than the other. The volume of the smaller pyramid is 216 inches cubed. The volume of the larger pyramid is 343 inches cubed.
There is 2 answers to this question!
216:343
6:7
72:98
648:1029
36:49
30:35
216:343 and 6:7
To find the scale factor between the smaller figure and the larger figure, divide the volume of the smaller figure by the volume of the larger figure.
Volume of the smaller pyramid: 216 inches cubed
Volume of the larger pyramid: 343 inches cubed
216:343
Simplifying the ratio, divide both numbers by their greatest common factor:
216 ÷ 7 = 30
343 ÷ 7 = 49
Therefore, the scale factor of the smaller figure to the larger figure is 30:49.
To find the scale factor of the smaller figure to the larger figure, we need to compare their volumes.
The given options are:
216:343
6:7
72:98
648:1029
36:49
30:35
To find the scale factor, we can divide the volume of the smaller pyramid by the volume of the larger pyramid.
Let's try each of the options and see if any of them give us the same result:
1. 216/343 = 0.630: This is not equal to any of the other options.
2. 6/7 = 0.857: This is not equal to any of the other options.
3. 72/98 = 0.735: This is not equal to any of the other options.
4. 648/1029 = 0.630: This is equal to the first option, 216:343.
5. 36/49 = 0.735: This is equal to the third option, 72:98.
6. 30/35 = 0.857: This is equal to the second option, 6:7.
Therefore, the two possible scale factors for the smaller figure to the larger figure are 216:343 and 6:7.