Question

Find the diameter and the circumference with a radius of 7.7 cm.

Answer 1

Hint: To solve the given question, we will first find out about the circle, its radius, its diameter and what the circumference of any circle is. After doing this, we will make use of the fact that the diameter of the circle is double in length to the radius of the circle. With the help of this, we will find the diameter. After this, we will calculate the circumference of the circle by applying the formula \[\text{Circumference}=2\pi r,\] where r is the radius of the circle. When we will put r = 7.7 cm, we will get the value of the circumference of the circle.

Complete step-by-step answer:
Before we start to solve the given question, we must know about some of the terms like the circle, its radius, its diameter, etc. The circle is a locus of points whose distance from a fixed point is constant. The fixed point is called the center and the constant distance is called the radius of the circle.
Now, we have to find the diameter of the circle. We know that the diameter of a circle is twice the radius of the circle.

We are given that the radius of the circle is 7.7 cm. Thus, the diameter will be given by
\[\text{Diameter}=2\times \text{radius}\]
\[\Rightarrow \text{Diameter}=2\times 7.7cm\]
\[\Rightarrow \text{Diameter}=15.4cm\]
Now, we have to calculate the circumference of the circle. The circumference of the circle is the length of the boundary of the circle. The circumference of the circle is given by the formula
\[\text{Circumference}=2\pi \left( \text{radius} \right)\]
\[\Rightarrow \text{Circumference}=2\times \dfrac{22}{7}\times 7.7\text{ }cm\]
\[\Rightarrow \text{Circumference}=2\times 22\times 1.1\text{ }cm\]
\[\Rightarrow \text{Circumference}=48.4\text{ }cm\].

Note: We can find the circumference of the circle with the help of the diameter also. If the diameter of a circle is d, then its circumference will be given by the formula shown.
\[\Rightarrow \text{Circumference}=\pi d\]
In our case, d = 15.4 cm.
\[\Rightarrow \text{Circumference}=\dfrac{22}{7}\times 15.4\text{ }cm\]
\[\Rightarrow \text{Circumference}=48.4\text{ }cm\]