The volume of the solid is the amount of space in it.
The points on the graph are (0,0) and (1,7)
The volume is given as:
V1 = 7
The scale factor is given as:
k
Let the new volume be V.
So, we have:
V = V1 * k^3
Substitute 7 for V1
V = 7k^3
Divide both sides by 7
k^3 = V/7
Take the cube root of both sides
k = (V/7)^1/3
Next, we test the options
a. (0,0)
k = (0/7)^1/3
k = 0 --- this is true
b. (1,1)
k = (1/7)^1/3
k = 0.05 --- this is false
c. (1,7)
k = (7/7)^1/3
k = 1 --- this is true
d (7, 1)
k = (1/7)^1/3
k = 0.05 --- this is false
e. (14,2)
k = (2/7)^1/3
k = 0.10 --- this is false
f. (49,2)
k = (2/7)^1/3
k = 0.10 --- this is false
g. (56,2)
k = (2/7)^1/3
k = 0.10 --- this is false
h (27,3)
k = (3/7)^1/3
k = 0.14 --- this is false
Hence, the points on the graph are (0,0) and (1,7)
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