volume of cylinders and composite 3D figures practice what is the volume of t h e c o m p o s i t e figure 2 yd 2 yd 2 yd 4.5 yard 2 yard
To find the volume of the composite figure, we need to break it down into simpler shapes and then calculate the volume of each shape separately.
The composite figure consists of two parts:
- A cylinder with a radius of 2 yards and a height of 4.5 yards
- A rectangular prism with dimensions 2 yards by 2 yards by 2 yards
1. Volume of the cylinder:
V_cylinder = πr^2h
V_cylinder = π(2)^2(4.5)
V_cylinder ≈ 56.55 cubic yards
2. Volume of the rectangular prism:
V_prism = lwh
V_prism = 2 x 2 x 2
V_prism = 8 cubic yards
Total volume of the composite figure:
V_total = V_cylinder + V_prism
V_total = 56.55 + 8
V_total ≈ 64.55 cubic yards
Therefore, the volume of the composite figure is approximately 64.55 cubic yards.