SOLUTION: Cone A is similar to cone B with a scale factor of 1/9. If cone A, the smaller of the two, has a volume of 10 cm3, what is the volume of cone B?

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Question 197499: Cone A is similar to cone B with a scale factor of 1/9. If cone A, the smaller of the two, has a volume of 10 cm3, what is the volume of cone B?
Answer by vleith(2825) About Me  (Show Source):
You can put this solution on YOUR website!
Start with the formula for the volume of a cone.
+V+=+%281%2F3%29%28pi%29r%5E2%2Ah
You are told that Cone B has dimensions that are scaled to 9 times the dimensions of cone A.
So, the radius on cone B is 9r and the height on cone B is 9h.
Thus the volume for cone B is
V%5Bb%5D+=+%281%2F3%29%2A%28pi%29%2A%289r%29%5E2+%2A9h
V%5Bb%5D+=+%281%2F3%29%28pi%29r%5E2%2Ah+%2A9%5E3
You are told Cone A has a volume of 10cm3.
You can also see that Cone B's volume is just 9%5E3 times that of Cone A.
So the volume of Cone B = 10*9^3 cm3