A mailbox is 15 inches long and 8 inches wide. The height of the mailbox before the curve is 6 inches. What is the volume of the mailbox? Use 3.14 for pi.
since the curved part is a semi-circle of radius 4,
(8*6 + π/2 * 4^2)*15 = 720+120π in^3
To find the volume of the mailbox, first, we need to identify the shape of the mailbox. Based on the given dimensions, the shape of the mailbox can be determined as a rectangular prism with a curving top.
The formula to calculate the volume of a rectangular prism is:
Volume = length * width * height.
However, since the mailbox has a curving top, we need to subtract the volume of the curved portion from the total volume.
To find the volume of the curved portion, we can consider it as a cylinder. The formula to calculate the volume of a cylinder is:
Volume of cylinder = π * radius^2 * height.
First, let's calculate the volume of the rectangular prism:
Volume of rectangular prism = length * width * height
= 15 inches * 8 inches * 6 inches
= 720 cubic inches.
Now, let's calculate the volume of the curved portion:
Radius of the curved portion = width / 2
= 8 inches / 2
= 4 inches.
Volume of the curved portion = π * radius^2 * height
= 3.14 * 4 inches * 4 inches * 6 inches
= 301.44 cubic inches (approx).
To find the volume of the mailbox, we need to subtract the volume of the curved portion from the volume of the rectangular prism:
Volume of mailbox = Volume of rectangular prism - Volume of curved portion
= 720 cubic inches - 301.44 cubic inches
= 418.56 cubic inches (approx).
Therefore, the volume of the mailbox is approximately 418.56 cubic inches.