What is the area of a circle formed by the intersection of a plane that is 24 mm from the center of a sphere whose radius is 30 mm.

Area=Pi*r^2 where

r^2=30^2-24^2
Draw an axial section of the sphere perpendicular to the plane

Is my answer 324 mm

did you forget the π ?

area = πr^2 = 18^2π = 324π

mm^2

To find the area of the circle formed by the intersection of the plane and the sphere, you can use the formula for the area of a circle.

The formula for the area of a circle is A = πr^2, where A is the area and r is the radius of the circle.

In this case, the radius of the sphere is 30 mm. The distance from the center of the sphere to the plane (also known as the height or depth of the plane) is 24 mm.

To find the radius of the circle formed by the intersection of the plane and the sphere, you can use the Pythagorean theorem.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, the radius of the sphere is the hypotenuse, and the distance from the center of the sphere to the plane is one of the other sides. The radius of the circle formed by the intersection of the plane and the sphere is the other side.

Using the Pythagorean theorem, you can find the radius of the circle:

r^2 = (radius of sphere)^2 - (distance from center to plane)^2
r^2 = 30^2 - 24^2
r^2 = 900 - 576
r^2 = 324
r = √324
r = 18

Now that we have the radius of the circle, we can use the formula for the area of a circle to find the area:

A = πr^2
A = π(18)^2
A = π(324)
A = 324π

So, the area of the circle formed by the intersection of the plane and the sphere is 324π square millimeters.