# Nakafa Framework: LLM

URL: https://nakafa.com/en/exercises/high-school/snbt/quantitative-knowledge/try-out/set-9/1

Exercises: Try Out - Set 9: Real exam simulation to sharpen your skills and build confidence. - Problem 1

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## Exercise 1

### Question

export const metadata = {
  title: "Problem 1",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/26/2025",
};

import { Graph } from "../graph";

<Graph title="Geometry Visualization" description="Large square, inscribed circle, and small square." />

If the area of the large square is <InlineMath math="256 \text{ cm}^2" />, then the circumference of the circle is...


### Choices

- [ ] $$7\pi\text{ cm}$$
- [ ] $$10\pi\text{ cm}$$
- [ ] $$12\pi\text{ cm}$$
- [ ] $$14\pi\text{ cm}$$
- [x] $$16\pi\text{ cm}$$

### Answer & Explanation

export const metadata = {
  title: "Solution to Problem 1",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/26/2025",
};

Given the area of the large square is <InlineMath math="256 \text{ cm}^2" />.

#### Finding the Side Length of the Large Square

The area of a square (<InlineMath math="A" />) is given by <InlineMath math="A = s^2" />.

<MathContainer>
  <BlockMath math="s^2 = 256" />
  <BlockMath math="s = \sqrt{256} = 16 \text{ cm}" />
</MathContainer>

#### Finding the Diameter of the Circle

Notice that the circle is inscribed in the large square, tangent to its sides. Therefore, the diameter of the circle (<InlineMath math="d" />) is equal to the side length of the large square.

<MathContainer>
  <BlockMath math="d = s = 16 \text{ cm}" />
</MathContainer>

#### Calculating the Circumference of the Circle

The circumference of a circle (<InlineMath math="C" />) is given by <InlineMath math="C = \pi d" />.

<MathContainer>
  <BlockMath math="C = \pi \cdot 16 = 16\pi \text{ cm}" />
</MathContainer>

Therefore, the circumference of the circle is <InlineMath math="16\pi \text{ cm}" />.


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