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 answer:

S =  75.3982 cm2
V =  37.6991 cm3

Step-by-step explanation:

v=4 cm S1:S2 = 3:5  S1 = π r2 S2 = π r s  3/5 =  π r sπ r2 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=53=0.6  S=S1+S2=28.2743+47.1239=75.3982 cm2
V=31 S1 v=31 28.2743 4=37.6991 cm3



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