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A student said that the volume of a cone with a 4-inch diameter is two times the volume of a cone with the same height and a 2-inch radius. What is the error?

Sagot :

Step-by-step explanation:

Let V be the volume of the cone.

The student says that, the volume of a cone with a 4-inch diameter is two times the volume of a cone with the same height and a 2-inch radius.

If diameter is 4 inch, radius = 2 inch

Volume of the cone,

[tex]V=\dfrac{\pi }{3}\times 2^2\times h\\\\V=\dfrac{4\pi h}{3}[/tex] .......(1)

If radius, r = 2 inch

New volume,

[tex]V=\dfrac{\pi }{3}\times 2^2\times h\\\\V=\dfrac{4\pi h}{3}[/tex] ....(2)

We can see that the volume in both case is same. Hence, the student is correct.