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A rocket consists of a right circular cylinder of height 20 m surmounted by a cone whose height and diameter are equal and whose radius is the same as that of the cylindrical section. What should this radius be (rounded to two decimal places) if the total volume is to be 700Ï€ 3 m3?

Respuesta :

lcmendozaf

Answer:

r=5.44m

Explanation:

The volume of the cylinder part is:

[tex]V1 = 20*\pi *r^2[/tex]

The volume of the cone part:

[tex]V2 = \pi*r^2*h2/3[/tex]    where h2 = 2*r according to the enunciate of the problem.

Replacing this value of h2:

[tex]V2=2/3*\pi*r^3[/tex]

Since the total volume must be 700*Ï€

V1+V2=700Ï€

[tex]20*\pi*r^2+2/3*\pi*r^3=700*\pi[/tex]

Solving to find the roots of this equation we get:

r1 = 5.44m;  r2 = -6.71m;  r3 = -28.73m  If we discard negative values, we can say that:

r = 5.44m

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