Jude says that the volume of a square pyramid with base edges of 12 in and a height of 10 in is equal to the volume of a cylinder with a radius of 6.77 in and a height of 10 in. Jude rounded his answers to the nearest whole numbers. Examine Jude's calculations. Is he correct?

To solve this question, we apply the formulas for the volume of a square pyramid and the cylinder, and verify if they are equal. Since the formulas yield different results, they are different and he is not correct.

Volume of a pyramid:

The volume of a pyramid, with base area and height h, is given by:

In a square pyramid, with edges e, we have that , and then:

Volume of a cylinder:

The volume of a cylinder, with radius r and height h, is given by:

Pyramid:

Edges of 12 and height of 10, which means that: . Thus

Cylinder:

Radius of 6.77, height of 10, so:

Is he correct?

Since the volumes are different, he is not correct.

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