Question

What is the volume?
what is the surface area?

Answer 1

The volume of the pyramid is 1,425 in³. Without the slant height, we cannot calculate the exact surface area. The relevant formulas for a pyramid involve base area and triangular faces.

To calculate the volume of a pyramid with a square base, we use the formula
`V = (1)/(3) * (base area) * (height)`.

The base area is the square of one of the sides of the base, so for a base side of 15 inches, the base area is
`15 in * 15 in = 225 in^2`. The height of the pyramid is given as 19 inches. Thus, the volume is
`V = (1)/(3) * 225 in^2 * 19 in = 1,425 in^3.`

For the surface area, a pyramid has the area of the base plus the areas of the four triangular faces. Each triangular face has an area of
`(1)/(2) * base side * slant height`.

Without the slant height, we cannot accurately calculate the surface area. If we had the slant height (which is different from the height), we could find the area of one triangle and multiply by four, then add the area of the base to get the total surface area.