A pyramid has a square base with sides length of b. The height of the pyramid is h. If the pyramid is enlarged by doubling the height while leaving the base unchanged, what is the effect on the volume of the pyramid?

Will the volume triple?
These are my choices:

a.The volume does not change
b.The volume doubles
c.The volume triples
d.The volume quadruples

Volume of original pyramid = (1/3)π(b^2)h

Volume of new pyramid = (1/3)π(b^)(2h) = (2/3)π(b^2)h

How do they compare ?

Do they double??

Yes,

they differ only by the 1/3 vs 2/3
and 2/3 is twice as large as 1/3

A pyramid has a volume of 24 and a base area of 12. What is the length of the altitude of the pyramid?

To answer this question, we need to understand the formula for calculating the volume of a pyramid. The volume of a pyramid is given by the formula: V = (1/3) * base area * height.

In this case, the base of the pyramid is a square with sides of length b, so the base area is given by the formula: base area = b^2.

If we double the height of the pyramid while leaving the base unchanged, the new height would be 2h.

Now, let's calculate the volume of the enlarged pyramid using the formula. The new volume, V', would be: V' = (1/3) * base area * (2h).

Substituting the values for the base area and the new height, we get: V' = (1/3) * b^2 * (2h).

Simplifying the expression, we have: V' = (2/3) * b^2 * h.

Comparing this with the original volume formula, we can see that the new volume (V') is (2/3) times the original volume (V).

Therefore, the effect on the volume of the pyramid when it is enlarged by doubling the height while leaving the base unchanged is that the volume doubles.

Therefore, the correct answer is: b. The volume doubles.