The sum of the circumference of the circle and the perimeter of square is 184 cm.
The diameter of the circle is 28 cm. What is the sum of the area of circle and square?
1. 784 𝑐𝑚²
2. 576 𝑐𝑚²
3. 616 𝑐𝑚²
4. 1192 𝑐𝑚²

Introduction to Circle and Square Area Calculation

Calculating the area of a circle and a square is a fundamental concept in geometry. Understanding how to compute these values is crucial for solving complex mathematical problems, especially in competitive exams like CSIR NET, DBT BET JRF, GATE Biotechnology, and IIT JAM.

In this article, we will solve a typical exam question involving the sum of the circumference of a circle and the perimeter of a square. This step-by-step explanation will clarify the concept and help you apply it effectively in exams.

Key Phrase: Sum of the Area of a Circle and a Square

✅ Question and Answer

Question:
The sum of the circumference of a circle and the perimeter of a square is 184 cm.
The diameter of the circle is 28 cm.
What is the sum of the area of the circle and the square?

1. 784 cm²
2. 576 cm²
3. 616 cm²
4. 1192 cm²

Correct Answer: ✔️ Option 3: 616 cm²

Explanation of the Problem

1. Given:

• Sum of the circumference of a circle and the perimeter of a square = 184 cm
• Diameter of the circle = 28 cm

2. Step-by-Step Calculation

(A) Find the Circumference of the Circle

The formula for the circumference of a circle is:

C=π×d

where:

• d=28 cm
• π=3.1416

C=3.1416×28=87.96cm

Therefore, the circumference of the circle = 87.96 cm

(B) Find the Perimeter of the Square

Let the side of the square be x.
The formula for the perimeter of a square is:

P=4×xP

According to the question,

87.96+4x=184

4x=184−87.96

4x=96.04

x=24.01cm

Therefore, the side of the square = 24 cm

(C) Find the Area of the Circle

The formula for the area of a circle is:

Acircle=πr2 

here:

• r=28/2
• =14 cm   

Acircle​=3.1416×14 X14 

Therefore, the area of the circle ≈ 616 cm²

(D) Find the Area of the Square

The formula for the area of a square is:

Asquare=x X x 

= 24x 24

Asquare​=576cm2

(E) Find the Sum of the Areas

Sum of the areas =

616+576=1192 cm2