A sphere has a radius of r. What is the area of a cross section taken at a distance of 1/2r from the center of the sphere?

A. 1/4r^2
B. 1/2r^2
C. 1/2pie(r)^2
D. 3/4pie(r)^2

Question

contestada

Respuesta :

MathPhys MathPhys · Answer 1 · 2020-03-22T22:43:56+01:00

Answer:

D. ¾ πr²

Step-by-step explanation:

If r is the radius of the sphere, and R is the radius of circular cross section, then:

r² = (½ r)² + R²

r² = ¼ r² + R²

¾ r² = R²

So the area of the circular cross section is:

A = πR²

A = ¾ πr²

Answer Link