A regular triangular pyramid is cut by 2 planes which are parallel to its base. The planes trisects the altitude of the pyramid. Volume of top, middle and bottom part is V1, V2 and V3 respectively. What is the value of V1 :V2 : V3?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4, i.e. 1 : 7 : 19
Height of the biggest cone = H
Radius of the biggest cone = R
AB = BD = DF = H/3
Using similarity,
Therefore, AB/BC = AD/DE = AF/FG
(H/3)/BC = H/R
BC = R/3 [AD/DE = AE/FG]
(2H/3)/DE = H/R
DE = 2R/3
V1 = 1/3 × π × (BC)2 × AB = πR2H/81
V2 = 8πR2H/81- πR2H/81= 7πR2H/81
V3 = 1/3 × πR2H - 8πR2H/81 = 19πR2H/81