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Question

The triangle ABC has angle B=90. When it is rotated about AB, it gives a cone of volume 800π. When it is rotated about BC, it gives a cone of volume 1920π. The length of AC is

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Solution


When rotated about AB,
13πx2y=800π (1)

When rotated about BC,
13πy2x=1920π (2)

Dividing (2) by (1), we get
yx=19280=125
y=125x (3)

Multiplying (1) and (2), we get
19π2x3y3=10323192π2
x3y3=1032332364=103233343
xy=10234=240
From (3), x125x=240
x2=20×5=100
x=10
y=125×10=24
AC=x2+y2=102+242=26

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