Quiz Answers with Explanations

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📚 Part 1: Multiple Choice — Answers & Explanations

1. A rectangular prism is 3 ft by 4 ft by 5 ft. What is its surface area?

94 ft² (Correct)

60 ft²

47 ft²

120 ft²

Explanation: Surface area = 2(lw + lh + wh) = 2(3·4 + 3·5 + 4·5) = 2(12 + 15 + 20) = 2·47 = 94 ft².

2. A cube has edge length 6 in. What is the volume?

36 in³

216 in³ (Correct)

72 in³

1296 in³

Explanation: Volume of a cube = side³ = 6³ = 216 in³.

3. A cylinder has radius 3 in and height 5 in. What is its volume?

15π in³

45π in³ (Correct)

9π in³

30π in³

Explanation: Volume = πr²h = π·3²·5 = π·9·5 = 45π in³ (≈ 141.37 in³).

4. Which formula gives the total surface area of a closed cylinder?

2πr² + 2πrh (Correct)

πr² + 2πrh

4πr² + πrh

2πr² + πrh

Explanation: Total surface area = area of two bases (2πr²) + lateral area (2πrh) = 2πr² + 2πrh.

✏️ Part 2: Short Answers — Answers & Explanations

5. Find the volume of a sphere with radius 3 in.

Answer: 36π in³. Explanation: Volume = (4/3)πr³ = (4/3)π·27 = 36π in³ (≈ 113.10 in³).

6. A rectangular pool is 20 ft long, 10 ft wide, and 6 ft deep. How many cubic yards of water does it hold?

Answer: 1200 ft³ = 1200 ÷ 27 ≈ 44.44 yd³. Explanation: Volume = 20·10·6 = 1200 ft³. Convert to cubic yards: 1 yd³ = 27 ft³, so 1200/27 ≈ 44.44 yd³.

7. A box is 8 in by 5 in by 2 in. If each dimension is doubled, how many times larger is the new volume?

Answer: 8 times larger. Explanation: Doubling each dimension scales volume by 2³ = 8 (original volume 8·5·2 = 80 in³; new volume 16·10·4 = 640 in³).

8. In one clear sentence, state the difference between surface area and volume.

Answer: Surface area measures the total area covering the outside of a 3-D object (in square units), while volume measures the amount of space it contains (in cubic units). Explanation: Surface area = sum of exterior faces; volume = capacity inside the shape.

🔎 Lesson Goals, Success Criteria & Supports

I can... solve routine problems involving surface area and volume of prisms, cylinders, spheres, and cubes.

Success criteria: I can choose and apply the correct formula, show units (in² or in³), and explain each calculation step.

Differentiation strategies: For learners who need support, provide step-by-step templates and worked examples; use manipulatives or labeled diagrams; allow calculators for arithmetic. For learners who need challenge, give multi-step problems combining surface area and volume, or ask for proofs about scaling.

Extension activities: Compare how surface area and volume change under different scale factors; design a real-world container minimizing material for a given volume.

Dyslexia-friendly reading options: Provide printed copies with increased spacing, sans-serif fonts, colored overlays if helpful, and audio recordings of the problems. Keep language simple and break explanations into short lines.