Question

mathematics class test: perimeter & circles

name: devora date: 24/06/26

section a: circles (use \\(\pi = 3.14\\))

1. a circle has a diameter of \\(5\text{ cm}\\). calculate the circumference.
2. a circle has a radius of \\(4\text{ m}\\). calculate the circumference.
3. a circle has a diameter of \\(12\text{ mm}\\). calculate the circumference.
4. a circle has a circumference of \\(31.4\text{ cm}\\). find the diameter.
5. a circle has a circumference of \\(62.8\text{ m}\\). find the radius.

section b: compound shapes

1. calculate the perimeter of a shape with sides: \\(10\text{ m}\\), \\(6\text{ m}\\), \\(8\text{ m}\\), \\(4\text{ m}\\), \\(6\text{ m}\\).
2. a compound shape has sides \\(2\text{ km}\\), \\(3\text{ km}\\), \\(1.5\text{ km}\\) and \\(2.5\text{ km}\\). find the perimeter.
3. calculate the perimeter: \\(150\text{ mm}\\), \\(120\text{ mm}\\), \\(90\text{ mm}\\), \\(60\text{ mm}\\).
4. a compound shape has missing side. total perimeter is \\(50\text{ cm}\\). known sides: \\(10\text{ cm}\\), \\(12\text{ cm}\\), \\(8\text{ cm}\\), \\(5\text{ cm}\\). find missing side.
5. calculate the perimeter of a shape with sides \\(7\text{ cm}\\), \\(3\text{ cm}\\), \\(9\text{ cm}\\), \\(6\text{ cm}\\) and \\(5\text{ cm}\\).

show all working clearly.

Explanation:

<pre_analysis>
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"skills_matched": [
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"needs_drawing": false,
"concepts_used": [],
"new_concepts": [
"Circumference of Circles",
"Perimeter of Polygons",
"Compound Shape Perimeter"
],
"current_concepts": [
"Circumference of Circles",
"Perimeter of Polygons",
"Compound Shape Perimeter"
]
}
</pre_analysis>

<reasoning>

Calculate circle circumferences and dimensions

\[

$$\begin{aligned} &\text{Q1: } C = \pi d = 3.14 \times 5\text{ cm} = 15.7\text{ cm} \\ &\text{Q2: } C = 2\pi r = 2 \times 3.14 \times 4\text{ m} = 25.12\text{ m} \\ &\text{Q3: } C = \pi d = 3.14 \times 12\text{ mm} = 37.68\text{ mm} \\ &\text{Q4: } d = \frac{C}{\pi} = \frac{31.4\text{ cm}}{3.14} = 10\text{ cm} \\ &\text{Q5: } r = \frac{C}{2\pi} = \frac{62.8\text{ m}}{2 \times 3.14} = 10\text{ m} \end{aligned}$$

\]

Calculate perimeters of compound shapes

\[

$$\begin{aligned} &\text{Q6: } P = 10 + 6 + 8 + 4 + 6 = 34\text{ m} \\ &\text{Q7: } P = 2 + 3 + 1.5 + 2.5 = 9\text{ km} \\ &\text{Q8: } P = 150 + 120 + 90 + 60 = 420\text{ mm} \\ &\text{Q9: } \text{Missing side} = 50 - (10 + 12 + 8 + 5) = 50 - 35 = 15\text{ cm} \\ &\text{Q10: } P = 7 + 3 + 9 + 6 + 5 = 30\text{ cm} \end{aligned}$$

\]
</reasoning>

<answer>

No.	Answer
2	\(25.12\text{ m}\)
3	\(37.68\text{ mm}\)
4	\(10\text{ cm}\)
5	\(10\text{ m}\)
6	\(34\text{ m}\)
7	\(9\text{ km}\)
8	\(420\text{ mm}\)
9	\(15\text{ cm}\)
10	\(30\text{ cm}\)

</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multi-part",
"knowledge_point": [
"Mathematics",
"Geometry",
"Circumference of Circles"
]
}
</post_analysis>

Answer:

<pre_analysis>
{
"quality": "clear",
"question_count": 10,
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"step_cot",
"table_formatter",
"explain_then_answer",
"quick"
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"needs_drawing": false,
"concepts_used": [],
"new_concepts": [
"Circumference of Circles",
"Perimeter of Polygons",
"Compound Shape Perimeter"
],
"current_concepts": [
"Circumference of Circles",
"Perimeter of Polygons",
"Compound Shape Perimeter"
]
}
</pre_analysis>

<reasoning>

Calculate circle circumferences and dimensions

\[

$$\begin{aligned} &\text{Q1: } C = \pi d = 3.14 \times 5\text{ cm} = 15.7\text{ cm} \\ &\text{Q2: } C = 2\pi r = 2 \times 3.14 \times 4\text{ m} = 25.12\text{ m} \\ &\text{Q3: } C = \pi d = 3.14 \times 12\text{ mm} = 37.68\text{ mm} \\ &\text{Q4: } d = \frac{C}{\pi} = \frac{31.4\text{ cm}}{3.14} = 10\text{ cm} \\ &\text{Q5: } r = \frac{C}{2\pi} = \frac{62.8\text{ m}}{2 \times 3.14} = 10\text{ m} \end{aligned}$$

\]

Calculate perimeters of compound shapes

\[

$$\begin{aligned} &\text{Q6: } P = 10 + 6 + 8 + 4 + 6 = 34\text{ m} \\ &\text{Q7: } P = 2 + 3 + 1.5 + 2.5 = 9\text{ km} \\ &\text{Q8: } P = 150 + 120 + 90 + 60 = 420\text{ mm} \\ &\text{Q9: } \text{Missing side} = 50 - (10 + 12 + 8 + 5) = 50 - 35 = 15\text{ cm} \\ &\text{Q10: } P = 7 + 3 + 9 + 6 + 5 = 30\text{ cm} \end{aligned}$$

\]
</reasoning>

<answer>

No.	Answer
2	\(25.12\text{ m}\)
3	\(37.68\text{ mm}\)
4	\(10\text{ cm}\)
5	\(10\text{ m}\)
6	\(34\text{ m}\)
7	\(9\text{ km}\)
8	\(420\text{ mm}\)
9	\(15\text{ cm}\)
10	\(30\text{ cm}\)

</answer>

<post_analysis>
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"subject": "Mathematics",
"question_type": "Multi-part",
"knowledge_point": [
"Mathematics",
"Geometry",
"Circumference of Circles"
]
}
</post_analysis>