Question

A 90° sector has been cut out of the disk with radius & cm. The radii of the part that remains are taped together,

without overlapping, to form the cone. Find the radius and altitude of the cone.

Answer 1

The radius of the original circle is r cm. The circumference of the original circle is 2πr cm. The length of the arc of the 90° sector is 1/4 of the circumference of the original circle, or (1/4)(2πr) = (πr)/2 cm.

The slant height of the cone is equal to the radius of the original circle, or r cm. The altitude of the cone can be found using the Pythagorean theorem, where a is the altitude, b is the radius of the base, and c is the slant height:

a^2 + b^2 = c^2
a^2 + r^2 = r^2
a^2 = 0
a = 0

Therefore, the altitude of the cone is 0 cm.

The radius of the base of the cone is equal to the length of the arc of the 90° sector, or (πr)/2 cm.

Therefore, the radius of the cone is (πr)/2 cm and the altitude of the cone is 0 cm.