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A scoop of ice cream, shaped like a sphere with a diameter of 6 cm, is placed in an ice cream cone with diameter 5 cm and height 12 cm. Is the cone big enough to hold all the ice cream if it melts? Explain.
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Jun 6, 2017
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A scoop of ice cream, shaped like a sphere with a diameter of 6 cm, is placed in an ice cream cone with diameter 5 cm and height 12 cm. Is the cone big enough to hold all the ice cream if it melts? Explain.
Mathematics
high-school
Evizaer
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Answer: The answer would be No
Seth Noble
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Jun 8, 2017
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Seth Noble
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The answer is no.
We need to calculate if the volume of the ice cream is equal or smaller than the volume of the ice cream cone.
The volume of the ice cream (sphere) is
V1 = 4/3 r³ π
d = 6
r = d/2 = 6/2 = 3
V1 = 4/3 * 3³ * 3.14 = 113.04 cm³
The volume of the ice cream cone is:
V2 = 1/3 r² h π
d = 5
r = d/2 = 5/2 = 2.5
h = 12
V2 = 1/3 * 2.5² * 12 * 3.14 = 78.5 cm³
Since the volume of the ice cream (V1) is bigger than the volume of the ice cream cone (V2), the cone is not big enough
to hold all the ice cream if it melts
Catheline
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Jun 10, 2017
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Catheline
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