The volume of the rectangular prism is 280 cubic cm. Its base has the area of 40 sq. cm. What is the volume of the pyramid inside the prism?

height = h = 280/40

V = (1/3)(40)(h)

the volume of any pointy thing with straight sides = (1/3) base area * height

To find the volume of the pyramid inside the prism, we first need to determine the dimensions of the pyramid.

Given that the base of the prism has an area of 40 sq. cm, we can find the dimensions of the base by taking the square root of the area. This gives us a length and width of √40 cm.

Next, we determine the height of the prism. Since the volume of the prism is given as 280 cubic cm, we divide this volume by the area of the base to get the height. So, the height of the prism is 280 cm³ ÷ 40 cm² = 7 cm.

Now that we have the dimensions of the prism (length, width, and height), we can calculate the volume of the pyramid inside the prism.

A pyramid is a third of a prism with the same base and height. So, the volume of the pyramid will be one-third of the volume of the prism.

Therefore, the volume of the pyramid inside the prism is (1/3) × 280 cm³.

Simplifying, we get the volume of the pyramid as 93.33 cubic cm (rounded to two decimal places).