Calculating the area of a circle with diameter d

For exercises involving the area of a circle given the diameter d, students often wonder how to approach them, which is a question that many students have when they first encounter this type of problem. To help students solve these problems more easily, we have provided detailed instructions below, inviting students to read along.

Calculating the area of a circle with diameter d

How to Calculate the Area of a Circle with Diameter d

1. Understanding the Diameter of a Circle

- The diameter is the longest distance between any two points on the circle.
- Symbols for diameter: d or D.
- The length of the diameter of a circle is twice the radius of the circle.
- Diameter calculation formula: d = 2.r.

Where: d is the diameter, r is the radius

2. How to Calculate the Area of a Circle Given Diameter d

Procedure : To solve exercises involving the diameter d to find the area of a circle, follow these two steps:

- Step 1: Knowing d, we find r using the formula: d = 2.r =>r = 1/2.d
- Step 2: After finding r, apply the formula for calculating the area of a circle: A = π.r². Substitute the given values, perform careful calculations to find the result.

Application Exercise :

Calculating the area of a circle given the diameter:

a) d = 0.8 m.
b) d = 20 dm.
c) d = 4.2 cm.

* Solution:

a) The radius of the circle is: r = 1/2. d => r = 0.8 : 2 = 0.4 (m).
The area of the circle is: A = π .r² => A = 3.14 x 0.4² = 0.5024 (m²).

b) The radius of the circle is: r = 1/2. d => r = 20 : 2 = 10 (dm).
The area of the circle is: A = π .r² => A = 3.14 x 10² = 314 (dm²).

c) The radius of the circle is: r = 1/2. d => r = 4.2 : 2 = 2.1 (cm).
The area of the circle is: A = π .r² => A = 3.14 x 2.1² = 13.8474 (cm²).

Other exercises :

1. Calculate the area of a circle given the diameter d:

a) d = 12 cm
b) d = 21.2 m
c) d = 10 dm
d) d = 9.8 cm

2. A round pizza has a diameter of 50 cm, calculate the area of the pizza.

(Students solve these exercises on their own)

In this article, we've guided students on how to calculate the area of a circle given the diameter d. Students can practice solving basic exercises based on our suggestions to reinforce their understanding of the topic.

Another way to calculate the area of a circle is by using the radius. It's similar to when you know the diameter d. Refer to the article on how to calculate the area of a circle with radius r for more information.