Grade 7 Math Test Prep: Surface Area and Volume Distinction

📚 Quick Study Guide

• 📐 Surface Area: The total area of all the faces of a 3D shape. Think of it as the amount of wrapping paper you'd need to cover the entire object.
• 📦 Volume: The amount of space a 3D object occupies. Think of it as how much water you could pour inside.
• 🧊 Units: Always remember to include the correct units! Surface area is measured in square units (e.g., $cm^2$, $m^2$), and volume is measured in cubic units (e.g., $cm^3$, $m^3$).
• ➗ Formulas for Rectangular Prism:
  • 📏 Surface Area: $2(lw + lh + wh)$, where $l$ = length, $w$ = width, and $h$ = height.
  • 🧊 Volume: $lwh$
• 🧪 Formulas for Cube:
  • 📏 Surface Area: $6s^2$, where $s$ = side length.
  • 🧊 Volume: $s^3$
• 🧮 Formulas for Cylinder:
  • 📏 Surface Area: $2\pi r^2 + 2\pi rh$, where $r$ = radius, and $h$ = height.
  • 🧊 Volume: $\pi r^2h$

✍️ Practice Quiz

1. What is the surface area of a rectangular prism with length 5 cm, width 3 cm, and height 2 cm?
   1. 20 $cm^2$
   2. 30 $cm^2$
   3. 52 $cm^2$
   4. 62 $cm^2$
2. What is the volume of a cube with side length 4 cm?
   1. 12 $cm^3$
   2. 16 $cm^3$
   3. 24 $cm^3$
   4. 64 $cm^3$
3. What is the surface area of a cube with side length 6 m?
   1. 36 $m^2$
   2. 144 $m^2$
   3. 216 $m^2$
   4. 288 $m^2$
4. What is the volume of a rectangular prism with length 8 m, width 4 m, and height 3 m?
   1. 32 $m^3$
   2. 64 $m^3$
   3. 96 $m^3$
   4. 128 $m^3$
5. What is the volume of a cylinder with radius 2 cm and height 5 cm? (Use $\pi = 3.14$)
   1. 31.4 $cm^3$
   2. 62.8 $cm^3$
   3. 125.6 $cm^3$
   4. 157 $cm^3$
6. What is the surface area of a cylinder with radius 3 cm and height 7 cm? (Use $\pi = 3.14$)
   1. 131.88 $cm^2$
   2. 188.4 $cm^2$
   3. 282.6 $cm^2$
   4. 376.8 $cm^2$
7. A rectangular prism has a volume of 120 $cm^3$. If its length is 6 cm and its width is 4 cm, what is its height?
   1. 3 cm
   2. 4 cm
   3. 5 cm
   4. 6 cm