https://file.aiquickdraw.com/mathbot/file/1726057325023q9a25z7v.jpg

The problem asks for the distance the extremity of the large hand of a clock moves in 20 minutes, given that the hand is 21 cm long.

To solve this, we can consider the movement of the clock's hand as part of a circular motion. Here's how we can proceed:

### Step 1: Find the fraction of a full rotation
In 60 minutes, the large hand of a clock completes a full circle (i.e., 360 degrees). So in 20 minutes, the hand completes:
\[
\frac{20}{60} = \frac{1}{3} \text{ of a full rotation.}
\]

### Step 2: Calculate the circumference of the circle
The circumference \(C\) of the circle traced by the clock's hand is given by the formula:
\[
C = 2\pi r,
\]
where \(r\) is the length of the clock's hand. Substituting \(r = 21 \text{ cm}\), we get:
\[
C = 2\pi \times 21 = 42\pi \text{ cm}.
\]

### Step 3: Calculate the distance moved in 20 minutes
Since the hand moves \( \frac{1}{3} \) of a full rotation in 20 minutes, the distance moved is:
\[
\text{Distance} = \frac{1}{3} \times 42\pi = 14\pi \text{ cm}.
\]
Using \( \pi \approx 3.1416 \), the distance is approximately:
\[
\text{Distance} \approx 14 \times 3.1416 = 43.98 \text{ cm}.
\]

Thus, the extremity of the clock's hand moves approximately **43.98 cm** in 20 minutes.

Would you like more details or have any questions? 

Here are five related questions:
1. How would the distance change if the hand were 30 cm long instead?
2. What is the distance traveled by the clock’s second hand in 15 seconds if it is 10 cm long?
3. How many degrees does the large hand cover in 5 minutes?
4. What is the relationship between the length of the hand and the distance traveled?
5. How much time would it take for the large hand to complete half of a circle?

**Tip:** Remember, in circular motion, the length of the hand determines the radius of the circle, and the angle covered determines the fraction of the circumference traveled.

Large hand of a clock is 21 cm long. How much distance does its extremity move in 20 minutes?

Calculate how far the large hand of a clock, 21 cm long, moves in 20 minutes. This problem involves geometry and circular motion, focusing on the circumference of a circle. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation