Two square pyramids have the same volume. For the first pyramid, the side length of the base is 5 in. and the height is 9 in. The second pyramid has a height of 1 in. What is the side length of the base of the second pyramid?

Thanks in advance!

Volume of first

= (1/3)(5^2)(9) = 75 cubic inches

2nd volume = 75
= (1/3)(b^2)(1) = b^2/3

b^2/3 = 75
b^2 = 225
b = √225 =15

Thanks for telling me how to do it Reiny! 'Preciate ya!

To find the side length of the base of the second pyramid, we can use the formula for the volume of a pyramid, which is given by:

Volume = (1/3) * Base Area * Height

Let's start by finding the volume of the first pyramid. We know that its side length of the base is 5 in. and its height is 9 in. Plugging these values into the formula, we get:

Volume of first pyramid = (1/3) * (5 in.)^2 * 9 in. = (1/3) * 25 in.^2 * 9 in. = 225 in.^3

Since we know that the volume of the second pyramid is the same as the first pyramid, we can equate their volumes:

225 in.^3 = (1/3) * Base Area * 1 in.

Now, we want to find the side length of the base of the second pyramid. Since the height of the second pyramid is 1 in., we can rewrite the equation as:

225 in.^3 = (1/3) * Base Area * 1 in. = (1/3) * Base Area

Multiplying both sides by 3 gives us:

675 in.^3 = Base Area

To find the side length of the base, we need to calculate the square root of the base area:

Side length of base = √(675 in.^3)

Calculating the square root, we find:

Side length of base = √(225 * 3) in. = 15√3 in.

Therefore, the side length of the base of the second pyramid is 15√3 inches.