Grade 7 Math Volume quiz

📚 Quick Study Guide

• 📐 Volume Basics: Volume is the amount of space a three-dimensional object occupies. It's measured in cubic units (e.g., $cm^3$, $m^3$, $in^3$).
• 🧊 Volume of a Rectangular Prism: The volume ($V$) of a rectangular prism is found by multiplying its length ($l$), width ($w$), and height ($h$). Formula: $V = lwh$
• 🔴 Volume of a Cube: Since all sides of a cube are equal (let's call the side length $s$), the volume is calculated as $V = s^3$.
• 🔺 Volume of a Triangular Prism: The volume ($V$) of a triangular prism is the area of its triangular base ($A$) multiplied by its height ($h$). Formula: $V = Ah$, where $A = \frac{1}{2}bh$ (with $b$ being the base of the triangle and $h$ being the height of the triangle).
• 🧮 Units Conversion: Remember to keep your units consistent. If dimensions are in cm, the volume will be in $cm^3$. Be careful when converting between units!
• 🤔 Problem Solving Tips: Draw diagrams when possible, label the dimensions clearly, and double-check your calculations.

Practice Quiz

1. What is the volume of a rectangular prism with length 5 cm, width 3 cm, and height 2 cm?
   1. 6 $cm^3$
   2. 10 $cm^3$
   3. 15 $cm^3$
   4. 30 $cm^3$
2. A cube has a side length of 4 inches. What is its volume?
   1. 12 $in^3$
   2. 16 $in^3$
   3. 64 $in^3$
   4. 256 $in^3$
3. What is the volume of a triangular prism with a base area of 20 $cm^2$ and a height of 5 cm?
   1. 25 $cm^3$
   2. 50 $cm^3$
   3. 100 $cm^3$
   4. 400 $cm^3$
4. A rectangular prism has a volume of 120 $m^3$. If the length is 6 m and the width is 4 m, what is the height?
   1. 5 m
   2. 10 m
   3. 20 m
   4. 30 m
5. A cube has a volume of 27 $cm^3$. What is the length of each side?
   1. 3 cm
   2. 6 cm
   3. 9 cm
   4. 27 cm
6. What is the volume of a rectangular prism with length 8 cm, width 2 cm, and height 3.5 cm?
   1. 13.5 $cm^3$
   2. 28 $cm^3$
   3. 56 $cm^3$
   4. 64 $cm^3$
7. A triangular prism has a base triangle with a base of 6 cm and a height of 4 cm. The prism's height is 10 cm. What is the volume?
   1. 60 $cm^3$
   2. 80 $cm^3$
   3. 120 $cm^3$
   4. 240 $cm^3$