The central angle of sector G is 32°. What is the probability that the spinner lands on G?




The probability that the spinner lands on sector G is based on the ratio of the angle of sector G to the total angle in a circle, which is 360°.

### Step 1: Calculate the Probability

Given:
- The central angle of sector G: \( 32^\circ \)
- The total angle of a circle: \( 360^\circ \)

The probability \( P \) that the spinner lands on sector G is calculated as:
\[
P(\text{G}) = \frac{\text{Angle of sector G}}{\text{Total angle of circle}} = \frac{32^\circ}{360^\circ}
\]

### Step 2: Simplify the Fraction

\[
P(\text{G}) = \frac{32}{360} = \frac{8}{90} = \frac{4}{45}
\]

So, the probability that the spinner lands on sector G is \( \frac{4}{45} \).

### Final Answer:
The probability that the spinner lands on sector G is \( \frac{4}{45} \).

Would you like more details or have any questions?

### Related Questions:
1. What is a central angle in a circle?
2. How do you calculate the area of a sector given the central angle and radius?
3. What is the relationship between the arc length and the central angle?
4. How would the probability change if the central angle were doubled?
5. What is the total probability for all sectors of a spinner?
6. How can you convert the probability into a decimal or percentage?
7. If the central angle were \(90^\circ\), what would the probability be?
8. What are some real-life examples where sector probabilities are applied?

### Tip:
Always simplify the fraction when calculating probabilities. This gives a clearer understanding and makes comparison with other probabilities easier.

Learn how to calculate the probability that a spinner lands on sector G with a detailed step-by-step solution. This problem covers key mathematical concepts such as probability in circle geometry. Suitable for students in Grades 6-8.

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