Question
Radius and height of a right circular cone are 36 cm and
48 cm respectively. Cone is divided horizontally into three parts. Height of uppermost part is 12 cm and height of lowermost part is 16 cm. Find the ratio of volume of uppermost part, middle part and lowermost part respectively. (Use Ï€ = 3) BC = 36 cm, AP = 12 cm and BD = 16 cmÂSolution
PD = 48 - 12 - 16 = 20 cm
∆APQ ~ ∆ABC (by AA similarity)
So, (PQ/BC) = (AP/AB)
Or, PQ = (12/48) × 36 = 9 cm
Again, ∆ADE ~ ∆ABC (by AA similarity)
So, (DE/BC) = (AD/AB)
Or, DE = (32/48) × 36 = 24 cm
Volume of uppermost part = (1/3) × 3 × 9² × 12 = 972 cm³
Volume of middle part = (1/3) × 3 × 24² × 32 - (1/3) × 3 × 9² × 12
= 18432 - 972 = 17460 cm³
Volume of lowermost part = (1/3) × 3 × 36² × 48 - (1/3) × 3 × 24² × 32
= 62208 - 18432 = 43776 cm³
Required ratio = 972:17460:43776 = 27:485:1216
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