How to Find the Volume of a Pyramid?

What is the formula for finding the volume of a pyramid?

How can we determine the volume of a pyramid using the given data?

Formula for Volume of Pyramid:

The volume of a pyramid can be calculated using the formula V = (1/3) * base area * height.

Finding the volume of a pyramid involves utilizing its base area and height. By multiplying the base area and height of the pyramid and then dividing the result by 3, we can determine the volume of the pyramid.

In this case, the formula V = (1/3) * 135 * h = 189 provides us with the volume of 189cm³ for pyramid X. To find the volume of pyramid Y, we need to consider the similarity between the two pyramids and their surface areas.

The surface area of pyramid Y is 240cm², while the surface area of pyramid X is 135cm². By calculating the ratio of their surface areas, we can determine the volume of pyramid Y. Using the ratio of 135/240, which simplifies to 9/16, we can find the volume of pyramid Y.

Since volume is proportional to the cube of the length scale factor between similar shapes, the volume of pyramid Y will be (9/16)^(3/2) times the volume of pyramid X, which is 189cm³. Calculating this yields approximately 120cm³ as the volume of pyramid Y.

Therefore, the volume of pyramid Y can be found using the concept of similarity between the two pyramids and ratios, resulting in an approximate volume of 120cm³.