A plane 5 cm from the center of a sphere intersects the sphere in a circle a with diameter 24 cm. What is the diameter of the sphere?

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Answer 1 · 2018-06-13T10:44:52

#color(blue)("Diameter of sphere"= 26 " cm")#

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From the diagram:

#CE# is the diameter of the sphere.

#OD=5cm# is the distance from the centre of the sphere to the plane.

#CO=r# radius of sphere.

#AB=24# is diameter of the circle formed by intersection of plane.

#AD=DB=12 cm#

#D# is the midpoint of #AB#

#CD=CO+5=r+5#

#DE=r-5#

Using the intersecting chords theorem:

#CDxxDE=ADxxDB#

#(r+5)(r-5)=12 xx12#

#r^2-25=144#

#r^2=169=>r=13#

Negative value not valid for radius.

Diameter of sphere is:

#r+5+r-5=2r=2(13)=26#

#color(blue)("Diameter of sphere"= 26 " cm")#