Unit 7 Volume of Composite 3D Figures Practice
1. Find the volume of the following composite figure:
The figure consists of a rectangular prism with dimensions 10 cm x 5 cm x 4 cm and a cylinder with a radius of 3 cm and a height of 8 cm.
To find the volume of the rectangular prism, use the formula V = l x w x h, where l is the length, w is the width, and h is the height.
V = 10 cm x 5 cm x 4 cm = 200 cm³
To find the volume of the cylinder, use the formula V = πr²h, where r is the radius and h is the height.
V = π x (3 cm)² x 8 cm = 72π cm³
Add the volumes of the rectangular prism and the cylinder to get the total volume of the composite figure:
Total volume = 200 cm³ + 72π cm³ ≈ 322.56 cm³
2. Find the volume of the following composite figure:
The figure consists of a cube with a side length of 6 cm and a hemisphere with a radius of 4 cm.
To find the volume of the cube, use the formula V = s³, where s is the side length.
V = (6 cm)³ = 216 cm³
To find the volume of the hemisphere, use the formula V = (2/3)πr³, where r is the radius.
V = (2/3)π x (4 cm)³ = 85.33 cm³
Add the volumes of the cube and the hemisphere to get the total volume of the composite figure:
Total volume = 216 cm³ + 85.33 cm³ = 301.33 cm³
3. Find the volume of the following composite figure:
The figure consists of a triangular prism with a base of 5 cm, height of 6 cm, and length of 8 cm, and a cone with a radius of 3 cm and height of 4 cm.
To find the volume of the triangular prism, use the formula V = (1/2)bh x l, where b is the base, h is the height, and l is the length.
V = (1/2) x 5 cm x 6 cm x 8 cm = 120 cm³
To find the volume of the cone, use the formula V = (1/3)πr²h, where r is the radius and h is the height.
V = (1/3)π x (3 cm)² x 4 cm = 12π cm³
Add the volumes of the triangular prism and the cone to get the total volume of the composite figure:
Total volume = 120 cm³ + 12π cm³ ≈ 158.85 cm³