Introduction
Volume of Prisms is an important Grade 7 math skill because students are moving from simple answers toward explaining how the math works.
In this lesson, students use models, real questions, worked examples, practice problems, and two online quizzes to build confidence with volume of prisms.
What Is Volume of Prisms?
Volume of Prisms means using units, estimates, and operations to solve measurement situations.
The goal is not only to get the answer. Students should be able to show the idea, explain the strategy, and check whether the answer makes sense.
Understanding Volume of Prisms
Before solving, students should slow down and decide what each number, shape, unit, or label represents.
- Read the question carefully and identify what is being asked.
- Choose a model, equation, table, or diagram that matches the situation.
- Solve one step at a time and keep units or labels attached.
- Use the answer explanation to check that the result makes sense.
Visual Models
Visual Model 1
Question: The rectangular prism shown has dimensions as labeled. What is its volume in cubic units?
- A. \(15\) cubic units
- B. \(60\) cubic units
- C. \(120\) cubic units
- D. \(240\) cubic units
Why it works: \(V = 6 \times 4 \times 5 = 120\) cubic units.
Answer: \(120\) cubic units
Visual Model 2
Question: A triangular prism has a right-triangular base with legs \(6\) inches and \(5\) inches, and the prism has a depth of \(12\) inches. What is the volume? (Area of a right triangle \(= \frac{1}{2} \times \text{leg}_1 \times \text{leg}_2\))
- A. \(90\) in\(^3\)
- B. \(180\) in\(^3\)
- C. \(360\) in\(^3\)
- D. \(720\) in\(^3\)
Why it works: Base area \(= \frac{1}{2} \times 6 \times 5 = 15\) in\(^2\). Volume \(= 15 \times 12 = 180\) in\(^3\).
Answer: \(180\) in\(^3\)
Worked Examples
Example 1
Question: A rectangular prism has the dimensions shown. What is its volume?
- A. \(28\) cm\(^3\)
- B. \(224\) cm\(^3\)
- C. \(504\) cm\(^3\)
- D. \(672\) cm\(^3\)
- \(V = l \times w \times h = 14 \times 8 \times 6 = 672\) cm\(^3\).
Answer: \(672\) cm\(^3\)
Example 2
Question: A trapezoidal prism has a trapezoidal base with parallel sides \(5\) cm and \(4\) cm, height \(3\) cm, and prism depth \(7\) cm. What is the volume?
- A. \(94.5\) cm\(^3\)
- B. \(115.5\) cm\(^3\)
- C. \(126\) cm\(^3\)
- D. \(189\) cm\(^3\)
- Base area \(= \frac{1}{2}(5 + 4) \times 3 = \frac{1}{2} \times 9 \times 3 = 13.5\) cm\(^2\).
- Volume \(= 13.5 \times 7 = 94.5\) cm\(^3\).
Answer: \(94.5\) cm\(^3\)
Example 3
Question: A right triangular prism has a right-triangular base with legs \(4\) m and \(3\) m and a depth of \(11\) m. What is the volume?
- A. \(18\) m\(^3\)
- B. \(36\) m\(^3\)
- C. \(66\) m\(^3\)
- D. \(132\) m\(^3\)
- Base area \(= \frac{1}{2} \times 4 \times 3 = 6\) m\(^2\).
- Volume \(= 6 \times 11 = 66\) m\(^3\).
Answer: \(66\) m\(^3\)
Real-World Word Problems
Problem 1
Question: A rectangular prism has a base area of \(24\) square inches and a height of \(6\) inches. Find the volume.
- A. \(288\) in\(^3\)
- B. \(144\) in\(^3\)
- C. \(72\) in\(^3\)
- D. \(30\) in\(^3\)
Why it works: \(V = B \times h = 24 \times 6 = 144\) in\(^3\).
Answer: \(144\) in\(^3\)
Problem 2
Question: A triangular prism has volume \(126\) cubic inches. If the triangular base has area \(18\) in\(^2\), what is the height of the prism?
- A. \(7\) in
- B. \(8\) in
- C. \(9\) in
- D. \(144\) in
Why it works: \(h = \frac{V}{B} = \frac{126}{18} = 7\) inches.
Answer: \(7\) in
Common Mistakes
- Rushing before identifying what the numbers represent.
- Choosing an operation that does not match the situation.
- Dropping labels, units, or context from the answer.
- Skipping the estimate or reasonableness check.
Strategy Tips
- Underline the question being asked.
- Use a model before jumping to computation.
- Write an equation that matches the story or picture.
- Explain the final answer in a sentence.
Practice Questions
Question 1
A triangular prism has a triangular base with area \(15\) cm\(^2\) and a height of \(10\) cm. What is its volume?
- A. \(25\) cm\(^3\)
- B. \(75\) cm\(^3\)
- C. \(150\) cm\(^3\)
- D. \(300\) cm\(^3\)
Question 2
A rectangular prism has dimensions \(5\) m, \(4\) m, and \(8\) m. What is its volume?
- A. \(320\) m\(^3\)
- B. \(160\) m\(^3\)
- C. \(40\) m\(^3\)
- D. \(17\) m\(^3\)
Question 3
A rectangular prism has length \(12\) cm, width \(5\) cm, and height \(3\) cm. Which expression correctly represents the volume?
- A. \((12 + 5) \times 3\)
- B. \(12 \times 5 \times 3\)
- C. \(2(12 + 5 + 3)\)
- D. \(12 + 5 + 3\)
Question 4
A rectangular prism has volume \(240\) cm\(^3\) and base area \(30\) cm\(^2\). What is the height of the prism?
- A. \(8\) cm
- B. \(10\) cm
- C. \(15\) cm
- D. \(210\) cm
Question 5
A rectangular prism with a volume of \(360\) m\(^3\) has a base area of \(40\) m\(^2\). Find the height.
- A. \(4\) m
- B. \(7\) m
- C. \(9\) m
- D. \(14400\) m
Question 6
Convert \(2\) cubic meters to cubic centimeters. (Hint: \(1\) m \(= 100\) cm)
- A. \(2 \times 10^6\) cm\(^3\)
- B. \(2 \times 10^8\) cm\(^3\)
- C. \(2 \times 10^{12}\) cm\(^3\)
- D. \(2 \times 10^9\) cm\(^3\)
Full Answer Explanations Click to show all answers and explanations
Question 1
Answer: \(150\) cm\(^3\)
Volume of a prism \(=\) base area \(\times\) height \(=15\times10=150\) cm\(^3\).
Question 2
Answer: \(160\) m\(^3\)
Volume \(= l \times w \times h = 5 \times 4 \times 8 = 160\) m\(^3\).
Question 3
Answer: \(180\) cm\(^3\)
Volume of a rectangular prism is length \(\times\) width \(\times\) height, so \(12 \times 5 \times 3 = 180\) cm\(^3\).
Question 4
Answer: \(8\) cm
Rearranging \(V = B \times h\), we get \(h = \frac{V}{B} = \frac{240}{30} = 8\) cm.
Question 5
Answer: \(9\) m
\(h = \frac{V}{B} = \frac{360}{40} = 9\) m.
Question 6
Answer: \(2 \times 10^6\) cm\(^3\)
\(1\) m \(= 100\) cm, so \(1\) m\(^3 = (100)^3 = 1{,}000{,}000\) cm\(^3 = 10^6\) cm\(^3\). Thus \(2\) m\(^3 = 2 \times 10^6\) cm\(^3\).
Connection to Standards
This lesson supports Grade 7 math expectations for reasoning, modeling, problem solving, and explaining answers clearly. It connects classroom skills to the kind of questions students see on state math assessments.
Summary
Volume of Prisms becomes easier when students connect the question to a model, use clear steps, and explain why the answer fits.
GOLDEN RULE
Understand the model before choosing the operation.
