Grade 8 math quiz: Volume of composite solids

📚 Quick Study Guide

• 🧱 Composite Solid: A 3D shape made up of two or more basic solids (e.g., cubes, prisms, cylinders, cones).
• 📐 Volume Formula Basics:
  • Cube: $V = s^3$ (where $s$ is the side length)
  • Rectangular Prism: $V = lwh$ (where $l$ is length, $w$ is width, $h$ is height)
  • Cylinder: $V = \pi r^2 h$ (where $r$ is the radius, $h$ is the height)
  • Cone: $V = \frac{1}{3} \pi r^2 h$ (where $r$ is the radius, $h$ is the height)
  • Sphere: $V = \frac{4}{3} \pi r^3$ (where $r$ is the radius)
• ➕ Calculating Volume: Find the volume of each individual solid, then add them together for the total volume of the composite solid.
• ➖ Hollow Sections: If a solid is hollow (e.g., a cylinder with a cylindrical hole), calculate the volume of the hollow part and subtract it from the volume of the larger solid.
• 📏 Units: Remember to express the volume in cubic units (e.g., $cm^3$, $m^3$, $in^3$).
• 💡 Tips: Draw diagrams and label dimensions clearly. Break down the composite solid into manageable parts.

🧪 Practice Quiz

1. What is the volume of a composite solid made of a cube with side 5 cm on top of a rectangular prism with length 8 cm, width 4 cm, and height 3 cm?
   1. A. 247 $cm^3$
   2. B. 200 $cm^3$
   3. C. 147 $cm^3$
   4. D. 196 $cm^3$
2. A composite solid consists of a cylinder (radius 3 cm, height 5 cm) with a cone on top (same radius, height 4 cm). What's the total volume?
   1. A. 188.50 $cm^3$
   2. B. 141.37 $cm^3$
   3. C. 150.00 $cm^3$
   4. D. 197.92 $cm^3$
3. A rectangular prism (6 cm x 4 cm x 2 cm) has a cylindrical hole drilled through it (radius 1 cm, length 6 cm). Find the remaining volume.
   1. A. 48 $cm^3$
   2. B. 29.15 $cm^3$
   3. C. 18.85 $cm^3$
   4. D. 66.85 $cm^3$
4. Calculate the volume of a solid comprising a hemisphere (radius 4 cm) placed on top of a cylinder (radius 4 cm, height 6 cm).
   1. A. 603.19 $cm^3$
   2. B. 402.12 $cm^3$
   3. C. 536.17 $cm^3$
   4. D. 804.25 $cm^3$
5. A composite solid is formed by joining two identical cubes, each with a side of 3 cm. What is the volume of the composite solid?
   1. A. 54 $cm^3$
   2. B. 27 $cm^3$
   3. C. 81 $cm^3$
   4. D. 108 $cm^3$
6. What's the volume of a structure made of a rectangular prism (5cm x 3cm x 2cm) attached to another rectangular prism (4cm x 2cm x 3cm)?
   1. A. 30 $cm^3$
   2. B. 24 $cm^3$
   3. C. 54 $cm^3$
   4. D. 60 $cm^3$
7. A shape consists of a cube (side 2cm) sitting on a larger cube (side 4cm). What is the volume of the entire shape?
   1. A. 8 $cm^3$
   2. B. 64 $cm^3$
   3. C. 72 $cm^3$
   4. D. 56 $cm^3$