Geometry help?

Question

The ratio of the base radius and height of a cone is 3:4. If the cost of smoothening the curved surface area at 5 cents per 1 sq cm is $115.50, then find the volume of the liquid contained in it.

please show all work and if possible, include a diagram. thanks in advance.

thanks for trying..

Answer 1

If the cost of sanding is 115.50, that's 115.50/0.5 cm^2 = 2310cm^2.

the surface area of a cone is pi*r*(r^2+h^2)^(1/2)
using the given ratio pi*r*(r^2+(4r/3)^2)^(1/2)
=pi*5*(r^2)/3 so r^2=(3*2310cm^2/(Pi*5))

V=(1/3)Pi(r^2)h= =(1/3)Pi(r^3)4/3=

(1/3)*Pi*4/3*(3*2310cm^2/ (Pi*5))^(3/2) = 13 liters