Geometry: Sphere

Question

A sphere of radius 5cm and a cone of base radius 5cm and height 10cm rests on a

horizontal table surface. A horizontal plane 3 cm above the surface cuts both solids.

a Find the radius of the circular cross-section of both the sphere and the cone.

b If points A and B are the endpoints of a diameter of a small circle, find the distance from A to B on a great circle which passes through A and B.

Please show workings :)

Answer 1

Answer 2

Start with the cone. Notice that the radius of a cone varies linearly with the height. At one end, the radius is 0, and at the other end it is-- for this problem--5cm at the base.

The base is 7cm from the small end and thus the radius will be 5cm * (7/10) = 3.5cm

For the sphere, draw the cross section. This will be a circle with a radius of 5cm with a chord 2cm from the center. Using the Pythagorean theorem, the radius of the cross-section is √(5² - 2²) = √21

The (b) question seems to be unrelated to all of this.....Start by looking up the definition of a "great circle"

Answer 3

Please show a diagram.