Grade 7 Math Volume of prisms examples

📚 Quick Study Guide

📐
• Prism Definition: A 3D shape with two identical ends (bases) and flat rectangular sides.
📏
• Volume Formula: The volume of a prism is found by multiplying the area of the base (B) by the height (h) of the prism: $V = B \times h$.
🧊
• Base Area: The formula for the base area (B) depends on the shape of the base. For example, if the base is a rectangle, then $B = length \times width$; if the base is a triangle, then $B = \frac{1}{2} \times base \times height$.
🔢
• Units: Volume is always measured in cubic units (e.g., $cm^3$, $m^3$, $in^3$).
💡
• Tips: Make sure all measurements are in the same units before calculating the volume. Identify the shape of the base correctly!

Practice Quiz

1. What is the volume of a rectangular prism with length 5 cm, width 3 cm, and height 4 cm?
   1. 12 $cm^3$
   2. 24 $cm^3$
   3. 60 $cm^3$
   4. 30 $cm^3$
2. A triangular prism has a base with an area of 20 $cm^2$ and a height of 6 cm. What is its volume?
   1. 60 $cm^3$
   2. 120 $cm^3$
   3. 80 $cm^3$
   4. 40 $cm^3$
3. What is the height of a rectangular prism with a volume of 100 $cm^3$, a length of 5 cm, and a width of 4 cm?
   1. 2 cm
   2. 4 cm
   3. 5 cm
   4. 10 cm
4. A cube has sides of length 3 inches. What is its volume?
   1. 9 $in^3$
   2. 12 $in^3$
   3. 18 $in^3$
   4. 27 $in^3$
5. What is the volume of a triangular prism if the base of the triangle is 8 cm, the height of the triangle is 5 cm, and the height of the prism is 10 cm?
   1. 400 $cm^3$
   2. 200 $cm^3$
   3. 130 $cm^3$
   4. 800 $cm^3$
6. A rectangular prism has a square base with sides of 6 cm and a height of 7 cm. What is its volume?
   1. 42 $cm^3$
   2. 84 $cm^3$
   3. 252 $cm^3$
   4. 168 $cm^3$
7. What happens to the volume of a prism if you double its height?
   1. The volume stays the same.
   2. The volume is halved.
   3. The volume is doubled.
   4. The volume is quadrupled.