Priyanshu has a motor cycle with wheels of diameter 91 cm. There are 22 spokes in the wheel. Find the length of arc between two adjoining spokes.

Options

A. 26cm
B. 13cm
C. 15cm
D. 18cm

Answer

To find the length of the arc between two adjoining spokes on Priyanshu's motorcycle wheel, we can follow these steps:

### Step 1: Find the circumference of the wheel
The circumference \( C \) of a circle is given by the formula:
\[ C = \pi \times d \]
where \( d \) is the diameter of the wheel.

Given that the diameter \( d \) is 91 cm, we can calculate the circumference:
\[ C = \pi \times 91 \]

### Step 2: Calculate the total circumference
Using the approximation \( \pi \approx \frac{22}{7} \):
\[ C = \frac{22}{7} \times 91 \]

### Step 3: Simplify the circumference calculation
Now, we can simplify:
\[ C = \frac{22 \times 91}{7} \]
Calculating \( 22 \times 91 \):
\[ 22 \times 91 = 2002 \]
Thus,
\[ C = \frac{2002}{7} \approx 286 \]

### Step 4: Find the length of the arc between two spokes
Since there are 22 spokes, the arc length \( L \) between two adjoining spokes can be calculated by dividing the total circumference by the number of spokes:
\[ L = \frac{C}{22} = \frac{286}{22} \]

### Step 5: Simplify the arc length calculation
Now, we simplify:
\[ L = 13 \]

### Final Answer
The length of the arc between two adjoining spokes is **13 cm**.

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