Lateral surface area

The ratio of the area of the base of the rotary cone to its lateral surface area is 3: 5. Calculate the surface and volume of the cone, if its height v = 4 cm.

Correct result:

S =  75.3982 cm2
V =  37.6991 cm3

Solution:

v=4 cm S1:S2=3:5  S1=πr2 S2=πrs  3/5=πr2πrs 3/5=r/s  s2=r2+v2 s2=(3/5s)2+v2  s=v/1(3/5)2=4/1(3/5)2=5 cm  r=3/5 s=3/5 5=3 cm  S1=π r2=3.1416 3228.2743 cm2 S2=π r s=3.1416 3 547.1239 cm2  k=S1/S2=28.2743/47.1239=35=0.6  S=S1+S2=28.2743+47.1239=75.3982 cm2
V=13 S1 v=13 28.2743 4=37.6991 cm3



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