CBSE Class 10 Answered

Figure shows two spheres just covered by a cone .

Let r be the radius of smaller sphere and R be the radius of larger sphere.

Let B and C are center of smaller sphere and larger sphere respectively.

Let us draw the radial lines BE and CF parallel to base of cone ,

It is to be noted here, E and F are points on surface of sphere but do not touch the lateral surface of cone.

By joining AE and AF , we get two similar right triangles ΔABE and ΔACF .

By the properties of similar triangles , we get

Let AB = h . Then above expression can be written as

Cone height = AD = h + r + 2R

Above expression is simplified as

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∠DAG = θ ( given)

DG/AD = tanθ

DG = AD tanθ

Hence base radius of cone is