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Knowledge Expert
· commented
· 1 Months ago
Yes you are right. we can solved it another way.
its volume V = (1/3)(π)(R²)(H) cu. units = (πR²H)/3
2) As the horizontal plane cuts the cone into two parts through the mid point of its axis, the height of the cone is divided into two equal parts, forming a top cone of height H/2 units. If the base radius of the top cone is r units, then r/(H/2) = R/H [Since the vertical angle of both are same].
Solving, r = R/2 units.
Hence volume of the small cone at the top = v = (1/3)(π){(R/2)²{(H/2) cu. units
Simplifying, v = (πR²H)/24 cu. units
So volume of the bottom part (frustum) = V - v = (πR²H)/3 - (πR²H)/24 = 7(πR²H)/24 cu. units
3) So ratio of their volumes, Top part : Bottom part = (πR²H)/24 : 7(πR²H)/24 = 1:7
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