A focused Grade 7 learning session for Volume of Prisms using visual models, worked examples, strategy guidance, and a short mastery check.
Student goal: I can solve problems involving volume of prisms.
Volume of Prisms is part of Grade 7 Measurement Geometry. This activity focuses on the central idea students need before they move into independent practice.
Students will build Grade 7 mastery of volume of prisms using models, equations, and test-style reasoning.
| What to notice | How to use it |
|---|---|
| Numbers, units, labels, diagrams, or graphs | Identify what each part represents before calculating. |
| The relationship in the problem | Connect the model to an equation, comparison, or explanation. |
Use the figures and worked questions in the practice set below as the visual model for this skill.
Read the first practice question slowly. Decide what the question is asking, choose a strategy, solve, and then compare your reasoning with the answer explanation.
For Volume of Prisms, a strong worked example should show the setup, the calculation or model, and a final answer that matches the context.
Many Grade 7 test questions use real situations. Look for quantities, units, rates, measures, expressions, or data values that connect the math to the story.
After solving, explain what the answer means in the situation, not just the number you calculated.
I can solve problems involving volume of prisms.
Use the warmup, guided question, practice set, and exit questions below to check whether this skill is ready or needs more practice.
Use scratch paper. The explanation matters more than simply seeing whether the choice is correct.
A triangular prism has a triangular base with area \(15\) cm\(^2\) and a height of \(10\) cm. What is its volume?
Answer C: \(150\) cm\(^3\)
Volume of a prism \(=\) base area \(\times\) height \(=15\times10=150\) cm\(^3\).
A rectangular prism has dimensions \(5\) m, \(4\) m, and \(8\) m. What is its volume?
Answer B: \(160\) m\(^3\)
Volume \(= l \times w \times h = 5 \times 4 \times 8 = 160\) m\(^3\).
A rectangular prism has a base area of \(24\) square inches and a height of \(6\) inches. Find the volume.
Answer B: \(144\) in\(^3\)
\(V = B \times h = 24 \times 6 = 144\) in\(^3\).
A rectangular prism has length \(12\) cm, width \(5\) cm, and height \(3\) cm. Which expression correctly represents the volume?
Answer B: \(12 \times 5 \times 3\)
Volume of a rectangular prism is length \(\times\) width \(\times\) height, so \(12 \times 5 \times 3 = 180\) cm\(^3\).
The rectangular prism shown has dimensions as labeled. What is its volume in cubic units?
Answer C: \(120\) cubic units
\(V = 6 \times 4 \times 5 = 120\) cubic units.
A rectangular prism has volume \(240\) cm\(^3\) and base area \(30\) cm\(^2\). What is the height of the prism?
Answer A: \(8\) cm
Rearranging \(V = B \times h\), we get \(h = \frac{V}{B} = \frac{240}{30} = 8\) cm.
A triangular prism has volume \(126\) cubic inches. If the triangular base has area \(18\) in\(^2\), what is the height of the prism?
Answer A: \(7\) in
\(h = \frac{V}{B} = \frac{126}{18} = 7\) inches.
A rectangular prism with a volume of \(360\) m\(^3\) has a base area of \(40\) m\(^2\). Find the height.
Answer C: \(9\) m
\(h = \frac{V}{B} = \frac{360}{40} = 9\) m.
Convert \(2\) cubic meters to cubic centimeters. (Hint: \(1\) m \(= 100\) cm)
Answer A: \(2 \times 10^6\) 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\(^3\).
Convert \(5{,}000\) cubic inches to cubic feet. (Hint: \(1\) ft \(= 12\) in, so \(1\) ft\(^3 = 1{,}728\) in\(^3\))
Answer A: \(2.89\) ft\(^3\)
\(\frac{5{,}000 \text{ in}^3}{1{,}728 \text{ in}^3 / \text{ft}^3} \approx 2.89\) ft\(^3\).
A rectangular prism has length \(8\) cm, width \(6\) cm, and height \(10\) cm. Convert its volume to liters if \(1\) liter \(= 1{,}000\) cm\(^3\).
Answer A: \(0.48\) L
\(V = 8 \times 6 \times 10 = 480\) cm\(^3 = 480 / 1000 = 0.48\) L.
