Question
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. = 216in^2
S.A. = 486in^2
V = 567in^3
S.A. = 216in^2
S.A. = 486in^2
V = 567in^3
Answers
GPT 3.5
Let the ratio of the surface areas be x:1, where x is the scale factor of the similar figures.
Solving for x:
216/x = 486/1
216 = 486x
x = 216/486
x = 2.25
Since volume is the cubic factor, the ratio of volumes will be x^3:
V_large/V_small = (2.25)^3
V_large/V_small = 11.39
Now, we know the volume of the larger figure V_large = 567in^3.
So, the volume of the smaller figure V_small can be found by:
567/V_small = 11.39
V_small = 567/11.39
V_small ≈ 49.74 in^3
Therefore, the volume of the smaller figure is approximately 49.74 in^3.
Solving for x:
216/x = 486/1
216 = 486x
x = 216/486
x = 2.25
Since volume is the cubic factor, the ratio of volumes will be x^3:
V_large/V_small = (2.25)^3
V_large/V_small = 11.39
Now, we know the volume of the larger figure V_large = 567in^3.
So, the volume of the smaller figure V_small can be found by:
567/V_small = 11.39
V_small = 567/11.39
V_small ≈ 49.74 in^3
Therefore, the volume of the smaller figure is approximately 49.74 in^3.
Related Questions
The surface areas of two similar figures are given. The volume of the larger figure is given. Find t...
The surface areas of two similar figures are given. The volume of the larger figure is given. Find t...
The surface areas of two similar figures are given. The volume of the larger figure is given. Find t...
The surface areas of two similar figures are given. The volume of the larger figure is given. Find t...