A cross-section of a sphere (when cut by a plane through its center) is a circle of area 100pi cm^2 what is the surface area of the sphere ?
since for a circle, a = pi r^2 = 100pi, r = 10
for a sphere, a = 4pi r^2 = 400pi
To find the surface area of a sphere, we need to know either the radius or the diameter of the sphere. However, in this case, we are given the area of a cross-section of the sphere.
We can solve this problem by using the formula for the area of a circle. The area of a circle is given by the formula A = πr^2, where A is the area and r is the radius of the circle.
Since the cross-section of the sphere is a circle with an area of 100π cm^2, we can equate the given area to the formula for the area of a circle:
100π cm^2 = πr^2
To find the radius, we can cancel out the π terms on both sides of the equation:
100 = r^2
Taking the square root of both sides of the equation, we find:
r = 10 cm
Now that we know the radius of the sphere is 10 cm, we can use the formula for the surface area of a sphere:
Surface Area = 4πr^2
Substituting the value of the radius, we get:
Surface Area = 4π(10^2)
Simplifying the expression, we get:
Surface Area = 4π(100)
Surface Area = 400π cm^2
Therefore, the surface area of the sphere is 400π cm^2.