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3 years ago

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A cone has a radius of 40 cm and a volume of 1875. what is the volume of a similar cone with a radius of 16 cm

1 answer:

nignag [31]3 years ago

5 0

The volume of a cone by definition is given by:
V = (pi * r ^ 2 * h) / (3)
Where,
r: radio
h: height
Clearing the height of the original cone we have:
h = (3 * V) / (pi * r ^ 2)
Substituting values:
h = (3 * 1875) / (pi * (40) ^ 2)
h = 1.119058194
We now look for the scale factor:
K = 16/40
Simplifying:
K = 4/10
K = 2/5
We apply the scale factor to the new volume:
V '= ((k ^ 3) * (pi * r ^ 2 * h)) / (3)
Substituting:
V '= (((2/5) ^ 3) * (pi * (16) ^ 2 * (1.119058194))) / (3)
V '= 19.2 cm ^ 3
Answer:
the volume of a similar cone with a radius of 16 cm is:
V '= 19.2 cm ^ 3

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Step-by-step explanation:

For this case we know that the random variable of interest is normally distributed with the following parameters:

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Part a

We want to find this probability:

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And using the normal distribution table or excel we got:

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And we can use the z score formula given by:

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And replacing we got:

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