Can anyone help me with this problem... please help?

Question

The most economicla proportions of for a right circular cone is to have its height three times as long as its diameter. What lateral area of the cone would produce a volume of 100cm^3?

please help me...

Answer 1

The lateral area is the area of the sides of the cone (i.e. excluding the base). If s = slant height, then the lateral area is π*d*s. The slant height is the hypotenuse of a right triangle of base d/2 and height h of the cone, so s = √[d^2/4 + h^2]. The lateral area is then

A = π*d*√[d^2/4 + h^2]

The volume of a cone is

V = (1/3)*π*(d^2/4)*h.

If this is an economical cone, then h = 3*d; put that into the formula for V:

V = (1/3)*π*(d^2/4)*3*d

V = π/4 * d^3;

solve for d.

Once you have d, you also have h ( = 3*d), you can put those values in the formula for lateral area to get your answer.

Answer 2

let the diameter be 2x and therefor the height is 6x.
Volume of cone = 1/3 * 22/7* (2x)²*6x.
you'll get x = 2.515. then work out the area. good luck

Answer 3

the volume of a RC cone is (pi)(r^2)h/3
given h=3d=6r,
V=2(pi)r^3=100cm^3...solve for r
r=(50/pi)^(1/3)cm
LA=pi*r*s where s is slant height
s= sqrt(37)*r
LA=(pi)(sqrt(37))(r^2)

when all is said and done i came up with 120.91 cm^2


Hope this helps

Answer 4

depends, are you talking about a cake cone or sugar cone.