Ch.13 (13.4)Surface Area and Volumes ! …
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Posted by Mayank Yadav ? 6 years, 11 months ago
- 4 answers
Anwaya Kumar Nayak 6 years, 11 months ago
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Gaurav Seth 6 years, 11 months ago
Solution: Volume of frustum will be equal to the volume of wire and by using this relation we can calculate the length of the wire.
In the given figure; AO = 20 cm and hence height of frustum LO = 10 cm
In triangle AOC we have angle CAO = 300 (halft of vertical angle of cone BAC)
Therefore;
tan30°=OCAO
Or, 1√3=OC20
Or, OC=20√3
Using similarity cirteria in triangles AOC and ALM it can be shown that LM=10√3(because LM bisects the cone through its height)
Similarly, LO = 10 cm
Volume of frustum can be calculated as follows:
V=13πh(r21+r22+r1r2)
=13π×10[(20√3)2+(10√3)2+20√3×10√3]
=13π×10(4003+1003+2003)
=70009 π cm3
Volume of cylinder is given as follows:
=πr2h
Or, π(132)2×h=70009 π
Or, h=70009×1024
=796444.44 cm=7964.4 m
3Thank You