What is the volume of the composite figure?
2 yd 2yd 2 yd 4.5yd 2yd 5n a sha*e 6f a rectangle
(1 point)
The volume of the composite figure cannot be determined as the shape of the composite figure is not specified.
a shape of a rectangle
To calculate the volume of the composite figure with a shape of a rectangle, we first need to calculate the volume of each individual shape and then add them together.
The composite figure consists of one rectangular prism and one half-cylinder.
1. Volume of the rectangular prism:
Volume = length x width x height
Volume = 2yd x 4.5yd x 2yd
Volume = 18yd³
2. Volume of the half-cylinder:
The formula for the volume of a cylinder is 1/2πr²h where r is the radius of the cylinder and h is the height.
In this case, the radius of the cylinder would be 2 yd (half of the width of the rectangle), and the height of the cylinder would be 4.5 yd.
Volume = 0.5 x π x (2yd)² x 4.5yd
Volume = 0.5 x π x 4yd² x 4.5yd
Volume = 9π yd³
Total volume of the composite figure:
Volume = Volume of rectangular prism + Volume of half-cylinder
Volume = 18yd³ + 9π yd³
Volume ≈ 18yd³ + 28.27 yd³
Volume ≈ 46.27 yd³
Therefore, the volume of the composite figure with a shape of a rectangle is approximately 46.27 cubic yards.