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

Did you find an error or inaccuracy? Feel free to write us. Thank you!

Tips for related online calculators
Check out our ratio calculator.
Tip: Our volume units converter will help you convert volume units.
See also our right triangle calculator.
See also our trigonometric triangle calculator.

You need to know the following knowledge to solve this word math problem:

We encourage you to watch this tutorial video on this math problem: video1   video2

Related math problems and questions: