Rotary cone

Rotary cone whose height is equal to the circumference of the base, has a volume 229 cm3.

Calculate the radius of the base circle and height of the cone.

Correct result:

r =  3.26 cm
h =  20.51 cm

Solution:

V=13πr2h=229 cm3 h=2πr  V=23π2r3  r=32Vπ23=3.26 cmV = \dfrac13 \pi r^2h = 229 \ cm^3 \ \\ h = 2 \pi r \ \\ \ \\ V = \dfrac23 \pi^2r^3 \ \\ \ \\ r = \sqrt[3]{ \dfrac32 \dfrac{V}{\pi^2}} = 3.26 \ \text{cm}
h=2πr=20.51 cmh = 2 \pi r = 20.51 \ \text{cm}



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