The Diameter Of The Circular Base Of A Round House Is 14 M. What Is The Circumference Of The Base Of The House? (Use The Value $\frac{22}{7}$ For $\pi$.)

Feb 25, 2025 by ADMIN 154 views

**The Diameter of a Round House: Calculating the Circumference**

Introduction

In mathematics, the circumference of a circle is a fundamental concept that is used to calculate the distance around a circular shape. The formula for calculating the circumference of a circle is given by C = 2πr, where C is the circumference and r is the radius of the circle. In this article, we will use the value of π as $\frac{22}{7}$ to calculate the circumference of the base of a round house with a diameter of 14 m.

Understanding the Problem

The problem states that the diameter of the circular base of a round house is 14 m. To calculate the circumference of the base, we need to use the formula C = 2πr. However, we are given the diameter of the circle, not the radius. We can use the relationship between the diameter and the radius to find the radius of the circle.

Calculating the Radius

The relationship between the diameter and the radius of a circle is given by d = 2r, where d is the diameter and r is the radius. We can rearrange this formula to solve for the radius: r = $\frac{d}{2}$ . Substituting the given value of the diameter, we get r = $\frac{14}{2}$ = 7 m.

Calculating the Circumference

Now that we have the radius of the circle, we can use the formula C = 2πr to calculate the circumference of the base of the round house. Substituting the value of the radius and the value of π as $\frac{22}{7}$ , we get C = 2 × $\frac{22}{7}$ × 7 = 44 m.

Conclusion

In this article, we used the value of π as $\frac{22}{7}$ to calculate the circumference of the base of a round house with a diameter of 14 m. We first calculated the radius of the circle using the relationship between the diameter and the radius, and then used the formula C = 2πr to calculate the circumference of the base. The result is a circumference of 44 m.

Real-World Applications

The calculation of the circumference of a circle has many real-world applications. For example, in architecture, the circumference of a circle is used to calculate the perimeter of a circular building or a circular wall. In engineering, the circumference of a circle is used to calculate the length of a circular pipe or a circular beam. In physics, the circumference of a circle is used to calculate the distance traveled by an object moving in a circular path.

Example Problems

Here are a few example problems that illustrate the calculation of the circumference of a circle:

A circular park has a diameter of 20 m. What is the circumference of the park?
A circular road has a diameter of 30 m. What is the circumference of the road?
A circular pipe has a diameter of 10 m. What is the circumference of the pipe?

Solutions to Example Problems

Here are the solutions to the example problems:

A circular park has a diameter of 20 m. To calculate the circumference of the park, we first calculate the radius of the park using the formula r = $\frac{d}{2}$ . Substituting the value of the diameter, we get r = $\frac{20}{2}$ = 10 m. Then, we use the formula C = 2πr to calculate the circumference of the park. Substituting the value of the radius and the value of π as $\frac{22}{7}$ , we get C = 2 × $\frac{22}{7}$ × 10 = 60 m.
A circular road has a diameter of 30 m. To calculate the circumference of the road, we first calculate the radius of the road using the formula r = $\frac{d}{2}$ . Substituting the value of the diameter, we get r = $\frac{30}{2}$ = 15 m. Then, we use the formula C = 2πr to calculate the circumference of the road. Substituting the value of the radius and the value of π as $\frac{22}{7}$ , we get C = 2 × $\frac{22}{7}$ × 15 = 90 m.
A circular pipe has a diameter of 10 m. To calculate the circumference of the pipe, we first calculate the radius of the pipe using the formula r = $\frac{d}{2}$ . Substituting the value of the diameter, we get r = $\frac{10}{2}$ = 5 m. Then, we use the formula C = 2πr to calculate the circumference of the pipe. Substituting the value of the radius and the value of π as $\frac{22}{7}$ , we get C = 2 × $\frac{22}{7}$ × 5 = 30 m.