The length of a minutes hand of a clock is 7 cm. The area swept by the minutes hand in 30 minutes is :

Options

A. 210 sq. cm
B. 154 sq. cm
C. 77 sq. cm
D. 147 sq. cm

Answer

To find the area swept by the minute's hand of a clock in 30 minutes, we can follow these steps:

### Step 1: Understand the Problem
The minute hand of a clock sweeps out an area in a circular motion. In 30 minutes, it covers half of a full circle.

### Step 2: Identify the Length of the Minute Hand
The length of the minute hand is given as 7 cm. This length serves as the radius (r) of the circular area swept by the minute hand.

### Step 3: Calculate the Area of a Full Circle
The formula for the area of a circle is:
\[ \text{Area} = \pi r^2 \]
Substituting the radius (r = 7 cm):
\[ \text{Area} = \pi \times (7)^2 = \pi \times 49 \]

### Step 4: Calculate the Area of a Semicircle
Since the minute hand sweeps out half of a full circle in 30 minutes, we need to divide the area of the full circle by 2:
\[ \text{Area of Semicircle} = \frac{\pi \times 49}{2} \]

### Step 5: Substitute the Value of \(\pi\)
Using \(\pi \approx \frac{22}{7}\):
\[ \text{Area of Semicircle} = \frac{\frac{22}{7} \times 49}{2} \]

### Step 6: Simplify the Expression
Calculating the area:
\[ = \frac{22 \times 49}{7 \times 2} = \frac{1078}{14} \]
Now simplifying:
\[ = \frac{539}{7} = 77 \text{ square centimeters} \]

### Final Answer
The area swept by the minute's hand in 30 minutes is **77 square centimeters**.

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