The radius of a circular object is the distance from the object's center to the outer limit of the object; for two-dimensional objects, namely the circle, the outer limit is its circumference, or perimeter, and for three-dimensional objects, namely the sphere, its outer limit is its surface area. The length of the radius is essential for calculating the volumes and areas of different geometric objects. Using different algebraic equations, you can find the square of the radius.

Square half of the diameter of a circle to find the radius squared. For example, the diameter is 30. Half of 30 is 15, and 15 squared is 225. The radius squared is 225.

Divide the area of a circle by π or pi to calculate the square of its radius. Pi is a math constant, which begins 3.14 and is unending. For example, dividing a circle area of 600 by π results in a radius squared of 190.99.

Multiply the height of a cylinder by π, and then divide that number into the cylinder's volume to find the radius squared. For example, a height of 7 multiplied by π equals 21.99. Dividing a volume of 300 by 21.99 results in a radius squared of 13.64.

Multiply the height of a cone by π and then divide that number into the cone's volume tripled to find the radius squared. For example, multiplying a height of 4 by π results in 12.57. If the cone's volume is 150, then multiplying it by 3 results in 450, and dividing 450 by 12.57 equals 35.81. The radius squared is 35.81.

Divide the surface area of a sphere by 4π to find the radius squared. For example, the sphere's surface area is 360. Dividing 360 by 4π, which is 12.57, results in 28.65. The radius squared is 28.65.