# Nakafa Framework: LLM

URL: https://nakafa.com/en/exercises/high-school/snbt/quantitative-knowledge/try-out/set-8/18

Exercises: Try Out - Set 8: Real exam simulation to sharpen your skills and build confidence. - Question 18

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## Exercise 18

### Question

export const metadata = {
  title: "Question 18",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/25/2025",
};

A hemispherical water container with a radius of <InlineMath math="15 \text{ cm}" /> is full of water. All the water in the container is transferred into a cylindrical container with a radius equal to the radius of the hemisphere. The height of the water in the cylindrical container is...


### Choices

- [x] $$10 \text{ cm}$$
- [ ] $$12 \text{ cm}$$
- [ ] $$18 \text{ cm}$$
- [ ] $$20 \text{ cm}$$
- [ ] $$22 \text{ cm}$$

### Answer & Explanation

export const metadata = {
  title: "Solution to Question 18",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/25/2025",
};

Since the water in the hemispherical container is transferred to the cylindrical container, the volume of water remains the same.

<MathContainer>
  <BlockMath math="V_{\text{hemisphere}} = V_{\text{cylinder}}" />
  <BlockMath math="\frac{1}{2} \cdot \frac{4}{3} \cdot \pi \cdot r^3 = \pi \cdot r^2 \cdot t" />
</MathContainer>

Since the radius of the sphere is the same as the radius of the cylinder, we can simplify the equation by dividing both sides by <InlineMath math="\pi \cdot r^2" />:

<MathContainer>
  <BlockMath math="\frac{2}{3} \cdot r = t" />
</MathContainer>

Given that the radius <InlineMath math="r = 15 \text{ cm}" />. We substitute this value into the equation:

<MathContainer>
  <BlockMath math="\frac{2}{3} \cdot 15 = t" />
  <BlockMath math="t = 10 \text{ cm}" />
</MathContainer>

Thus, the height of the water in the cylinder is <InlineMath math="10 \text{ cm}" />.


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