Question

Each of four circles has a radius of 4 inches. A larger circle has an area equal to the total area of the four smaller circles. What is the length of the radius, in inches, of the larger circle?

Answer 1

The radius of the larger circle is 8 inches

What is a circle?

A circle is a round plane shape, whose circumference consists of points equidistant from a fixed point.

To calculate the radius of the larger circle, we use the formula below.

Formula:

• A = 4A'............. Equation 1

Where:

• A = Area of the larger circle
• A' = Area of the smaller circle.

But,

• A = πR².............. Equation 2
• A' = πr²........... Equation 3

Where:

• R = Radius of the larger circle
• r = radius of the smaller circle.

Substitute equations 2 and 3 into equation 1

• πR² = 4πr²
• R² = 4r²
• R = 2r .............. Equation 4

Given:

• r = 4 inches

Substitute this value into equation 4

• R = 2×4
• R = 8 inches

Hence, The radius of the larger circle is 8 inches.

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