Real world examples of composite 3D figure volume problems

📚 Quick Study Guide

📐 Composite 3D figures are solids made up of two or more basic solids like cubes, prisms, cylinders, cones, and pyramids. ➗ To find the volume of a composite figure, break it down into its basic solid components. ➕ Calculate the volume of each individual component using the appropriate formula. 📝 Add the volumes of all the components together to find the total volume of the composite figure. 📏 Remember to use consistent units of measurement throughout your calculations. 💡 For figures with hollow sections, subtract the volume of the hollow section from the volume of the larger solid. ✏️ Common formulas:
• Cube: $V = s^3$, where $s$ is the side length.
• Rectangular Prism: $V = lwh$, where $l$ is length, $w$ is width, and $h$ is height.
• Cylinder: $V = \pi r^2 h$, where $r$ is the radius and $h$ is the height.
• Cone: $V = \frac{1}{3} \pi r^2 h$, where $r$ is the radius and $h$ is the height.
• Sphere: $V = \frac{4}{3} \pi r^3$, where $r$ is the radius.
• Pyramid: $V = \frac{1}{3}Bh$, where $B$ is the area of the base and $h$ is the height.

Practice Quiz

1. What is the first step in finding the volume of a composite 3D figure?
   1. A. Calculate the total surface area.
   2. B. Break the figure down into its basic solid components.
   3. C. Measure the weight of the figure.
   4. D. Estimate the volume by observation.
2. A composite figure consists of a cube with side length 5 cm and a cylinder with radius 2 cm and height 5 cm on top of the cube. What is the approximate volume of the composite figure?
   1. A. 125 $cm^3$
   2. B. 187.8 $cm^3$
   3. C. 62.8 $cm^3$
   4. D. 250 $cm^3$
3. A building is shaped like a rectangular prism with dimensions 20m x 15m x 8m, with a half-cylinder roof on top (radius 7.5m, length 20m). What is the approximate volume of the building?
   1. A. 2400 $m^3$
   2. B. 3534 $m^3$
   3. C. 4800 $m^3$
   4. D. 1134 $m^3$
4. A grain silo is composed of a cylinder and a cone on top of each other. If the cylinder has a radius of 5 ft and a height of 20 ft, and the cone has the same radius and a height of 6 ft, what is the total volume of the silo?
   1. A. 1570 $ft^3$
   2. B. 1963.5 $ft^3$
   3. C. 2356 $ft^3$
   4. D. 785.4 $ft^3$
5. What is the volume of a composite figure made of a rectangular prism (4cm x 3cm x 2cm) with a triangular prism (base=4cm, height=3cm, length=2cm) removed from the top?
   1. A. 24 $cm^3$
   2. B. 12 $cm^3$
   3. C. 36 $cm^3$
   4. D. 6 $cm^3$
6. A snowman is made by stacking three spheres. The bottom sphere has a radius of 30cm, the middle sphere has a radius of 20cm, and the top sphere has a radius of 10cm. What is the total volume of the snowman (approximately)?
   1. A. 113,097 $cm^3$
   2. B. 452,389 $cm^3$
   3. C. 169,730 $cm^3$
   4. D. 226,194 $cm^3$
7. A mold for candles is made by combining a cube (side length 8cm) and a square pyramid on top of the cube. The base of the pyramid is the same as the top of the cube and the height of the pyramid is 6cm. What is the volume of the candle mold?
   1. A. 512 $cm^3$
   2. B. 630 $cm^3$
   3. C. 128 $cm^3$
   4. D. 384 $cm^3$