2x cone

Circular cone height 84 cm was cut plane parallel with the base. The volume of these two small cones is the same. Calculate the height of the smaller cone.

Correct answer:

v2 =  66.6708 cm

Step-by-step explanation:

v1​=84 cm r1​=1 cm V1​=31​⋅ π⋅ r12​⋅ v1​=31​⋅ 3.1416⋅ 12⋅ 84≐87.9646 cm3  V2​=V1​/2=87.9646/2≐43.9823 cm3 r1​:v1​ = r2​:v2​  V2​ = 31​ ⋅  π ⋅ r22​ ⋅  v2​ V2​ = 31​ ⋅  π ⋅ (r1​/v1​⋅ v2​)2 ⋅  v2​ V2​ = 31​ ⋅  π ⋅ r12​/v12​⋅ v23​  v2​=33⋅ V2​/π/r12​⋅ v12​​=33⋅ 43.9823/3.1416/12⋅ 842​≐66.6708 cm  r2​=r1​/v1​⋅ v2​=1/84⋅ 66.6708≐0.7937 cm  V3​=31​⋅ π⋅ r22​⋅ v2​=31​⋅ 3.1416⋅ 0.79372⋅ 66.6708≐43.9823 cm3 V3​=V2​ = V1​/2

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