10. A sphere is inscribed in a right circular cone whose slant height has a length equal to that of the diameter of its base. What is the length of the radius of the sphere if the slant height and the diameter of the cone both measure 12 cm?

10. A sphere is inscribed in a right circular cone whose slant height has a length equal to that of the diameter of its base. What is the length of the radius of the sphere if the slant height and the diameter of the cone both measure 12 cm?

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter9: Surfaces And Solids

Section9.3: Cylinders And Cones

Problem 36E: For a right circular cone, the slant height has a measure equal to twice that of the radius length...

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Concept explainers

Cylinders

A cylinder is a three-dimensional solid shape with two parallel and congruent circular bases, joined by a curved surface at a fixed distance. A cylinder has an infinite curvilinear surface.

Cones

A cone is a three-dimensional solid shape having a flat base and a pointed edge at the top. The flat base of the cone tapers smoothly to form the pointed edge known as the apex. The flat base of the cone can either be circular or elliptical. A cone is drawn by joining the apex to all points on the base, using segments, lines, or half-lines, provided that the apex and the base both are in different planes.

Question

10. A sphere is inscribed in a right circular cone whose slant height has a
length equal to that of the diameter of its base. What is the length of the
radius of the sphere if the slant height and the diameter of the cone both
measure 12 cm?
12 cm
-12 cm–

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