Question

What is the radius of circle ?

Answer 1

Step 1: Recall the Relationship:
The radius of a circle is always half of its diameter.

\[ r = \frac{d}{2} \]
Step 2: Substitute the Given Value:
Diameter \( d = 35 \text{ mm} \).

\[ r = \frac{35}{2} \]
Step 3: Simplify:
\[ r = 17.5 \text{ mm} \]
Step 4: Final Answer:
\[ \boxed{\text{Radius} = 17.5 \text{ mm}} \]

Answer 2

Step 1: Recall the Formula:
The circumference of a circle represents the total boundary length around it.

\[ C = \pi d \quad \text{or} \quad C = 2\pi r \] Here, we will use \( C = \pi d \).

Step 2: Substitute the Given Values:
Diameter \( d = 35 \text{ mm} \)
Take \( \pi = \frac{22}{7} \).

\[ C = \frac{22}{7} \times 35 \]
Step 3: Simplify:
\[ C = 22 \times 5 \] \[ C = 110 \text{ mm} \]
Step 4: Final Answer:
\[ \boxed{\text{Circumference} = 110 \text{ mm}} \]

Answer 3

Step 1: Understand the Requirement:
The total wire length includes:
• The circular boundary (circumference)
• The 5 internal diameters

Step 2: Write the Formula:
\[ \text{Total Length} = \text{Circumference} + (5 \times \text{Diameter}) \]
Step 3: Substitute the Given Values:
Circumference \( = 110 \text{ mm} \)
Diameter \( = 35 \text{ mm} \)

Length of 5 diameters: \[ 5 \times 35 = 175 \text{ mm} \]
Step 4: Calculate Total Wire Length:
\[ L = 110 + 175 \] \[ L = 285 \text{ mm} \]
Step 5: Final Answer:
\[ \boxed{\text{Total wire required} = 285 \text{ mm}} \]

Answer 4

Step 1: Recall the Concept:
When a circle is divided into 10 equal sectors, each sector has one-tenth of the total area of the circle.

Step 2: Write the Formula:
\[ \text{Area of circle} = \pi r^2 \] \[ \text{Area of one sector} = \frac{\pi r^2}{10} \]
Step 3: Substitute the Given Radius:
Radius \( r = \frac{35}{2} \text{ mm} \)

\[ \text{Area of circle} = \frac{22}{7} \times \frac{35}{2} \times \frac{35}{2} \] \[ = \frac{22}{7} \times \frac{1225}{4} \] \[ = \frac{22 \times 175}{4} \] \[ = \frac{3850}{4} \] \[ = 962.5 \text{ mm}^2 \]
Step 4: Find Area of Each Sector:
\[ \text{Area of each sector} = \frac{962.5}{10} \] \[ = 96.25 \text{ mm}^2 \]
Step 5: Final Answer:
\[ \boxed{\text{Area of each sector} = 96.25 \text{ mm}^2} \]