Real-world examples of decomposing prisms for volume

📚 Quick Study Guide

🔢 Prism Volume Formula: The volume, $V$, of a prism is given by the formula: $V = A \times h$, where $A$ is the area of the base and $h$ is the height of the prism. 📐 Types of Prisms: Prisms are named after the shape of their bases (e.g., triangular prism, rectangular prism, pentagonal prism). 🧱 Decomposing Prisms: Complex shapes can be broken down into simpler prisms to calculate the total volume. This involves identifying the individual prisms and summing their volumes. 📏 Units: Always ensure that all measurements are in the same units before calculating the volume. Volume is expressed in cubic units (e.g., $cm^3$, $m^3$). 💡 Real-World Applications: Understanding prism volume is useful in fields like construction, architecture, and engineering for calculating material requirements.

🧪 Practice Quiz

1. What is the volume of a triangular prism with a base area of 25 $cm^2$ and a height of 10 cm?
   1. 50 $cm^3$
   2. 125 $cm^3$
   3. 250 $cm^3$
   4. 375 $cm^3$
2. A rectangular prism is made up of two smaller rectangular prisms. The first has dimensions 2 cm x 3 cm x 4 cm, and the second has dimensions 2 cm x 3 cm x 5 cm. What is the total volume?
   1. 36 $cm^3$
   2. 48 $cm^3$
   3. 54 $cm^3$
   4. 60 $cm^3$
3. A swimming pool has the shape of a trapezoidal prism. The parallel sides of the trapezoid are 8m and 12m, the height of the trapezoid is 5m, and the depth (height of prism) of the pool is 2m. What is the volume of water the pool can hold?
   1. 50 $m^3$
   2. 100 $m^3$
   3. 150 $m^3$
   4. 200 $m^3$
4. A candy box is a pentagonal prism. If you divide it into a rectangular prism and a triangular prism, and their volumes are 80 $cm^3$ and 20 $cm^3$ respectively, what is the volume of the original candy box?
   1. 40 $cm^3$
   2. 60 $cm^3$
   3. 100 $cm^3$
   4. 160 $cm^3$
5. A Toblerone chocolate bar can be seen as a triangular prism. It has a base that is an equilateral triangle with sides of length 4 cm and a height of 3 cm. The length of the chocolate bar is 20 cm. What is its volume?
   1. 60 $cm^3$
   2. 120 $cm^3$
   3. 240 $cm^3$
   4. 480 $cm^3$
6. A prism-shaped container is filled with sand. The base area is 30 $cm^2$ and the height is 12 cm. If half of the sand is removed, what is the volume of the remaining sand?
   1. 90 $cm^3$
   2. 180 $cm^3$
   3. 360 $cm^3$
   4. 720 $cm^3$
7. A complex prism is decomposed into three identical rectangular prisms each with volume 45 $cm^3$. What is the volume of the original complex prism?
   1. 15 $cm^3$
   2. 90 $cm^3$
   3. 135 $cm^3$
   4. 180 $cm^3$