Volume of Composite 3D Figures Practice

Answer 1

1. Find the volume of a composite figure made up of a rectangular prism and a cylinder. The dimensions are as follows:
- Rectangular prism: length = 5 cm, width = 3 cm, height = 4 cm
- Cylinder: radius = 2 cm, height = 6 cm

To find the volume of the rectangular prism, use the formula V = lwh:
V_rectangular prism = 5 cm * 3 cm * 4 cm = 60 cm^3

To find the volume of the cylinder, use the formula V = πr^2h:
V_cylinder = π * (2 cm)^2 * 6 cm = 24π cm^3 ≈ 75.4 cm^3

Therefore, the total volume of the composite figure is:
V_total = V_rectangular prism + V_cylinder
V_total = 60 cm^3 + 75.4 cm^3
V_total ≈ 135.4 cm^3

2. Find the volume of a composite figure made up of a cone and a hemisphere. The dimensions are as follows:
- Cone: radius = 4 cm, height = 8 cm
- Hemisphere: radius = 4 cm

To find the volume of the cone, use the formula V = (1/3)πr^2h:
V_cone = (1/3) * π * (4 cm)^2 * 8 cm = 85.33 cm^3

To find the volume of the hemisphere, use the formula V = (2/3)πr^3:
V_hemisphere = (2/3) * π * (4 cm)^3 = 33.51 cm^3

Therefore, the total volume of the composite figure is:
V_total = V_cone + V_hemisphere
V_total = 85.33 cm^3 + 33.51 cm^3
V_total ≈ 118.84 cm^3

3. Find the volume of a composite figure made up of a cube and a pyramid. The dimensions are as follows:
- Cube: side length = 6 cm
- Pyramid: base side length = 4 cm, height = 5 cm

To find the volume of the cube, use the formula V = s^3:
V_cube = (6 cm)^3 = 216 cm^3

To find the volume of the pyramid, use the formula V = (1/3)lwh:
V_pyramid = (1/3) * 4 cm * 4 cm * 5 cm = 26.67 cm^3

Therefore, the total volume of the composite figure is:
V_total = V_cube + V_pyramid
V_total = 216 cm^3 + 26.67 cm^3
V_total ≈ 242.67 cm^3

These are examples of how to find the volume of composite 3D figures by calculating the volumes of individual shapes and adding them together.