A block of marble is in the shape of a rectangular prism. The block is going to be cut into a pyramid. The prism has dimensions of 24 inches long, 36 inches wide, and 90 inches high. What is the volume of the newly cut pyramid block?
The volume of the block is _______ cubic inches.
To calculate the volume of the newly cut pyramid block, we need to first determine the volume of the original rectangular prism and then divide it by 3 (since we are cutting it into a pyramid).
The formula to calculate the volume of a rectangular prism is:
Volume = length * width * height
Given that the dimensions of the original block are 24 inches long, 36 inches wide, and 90 inches high, we can substitute these values into the formula:
Volume of rectangular prism = 24 inches * 36 inches * 90 inches
Now, let's solve for the volume:
Volume of rectangular prism = 24 * 36 * 90 cubic inches
= 77760 cubic inches
Since we are cutting the rectangular block into a pyramid, we need to divide the volume by 3:
Volume of pyramid block = (Volume of rectangular prism) / 3
= 77760 cubic inches / 3
= 25920 cubic inches
Therefore, the volume of the newly cut pyramid block is 25920 cubic inches.