contestada

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?

Respuesta :

asuwafohjames

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.

Learn more about circle here: https://brainly.com/question/22965557

Otras preguntas