a cone has a radius of 15 cm and a volume of 540cm. what is the volume of a similar cone with a radius of 10cm

The answer would be C. 160 cm^3

The Volume of a cone is given by

V = (1/3) * pi*r^2*h

We know V = 540 cm^3 and that radius (r) = 15 cm and can substitute into the equation to find h, which is the height of the cone.

I am going to leave the units off, but you should include it in your work.

540 = (1/3) * pi * (15) ^2*h

Solving for the height gives out

h=2.292 cm

According to your question. Now a similar cone will have the same ratio

h1/r1 = h2/r2

(2.292 / 15) = (h2 / 10) and solve for h2.

h2 = 1.528 cm

Substitute this into the Volume of a cone equation.

V = (1/3) * pi*r^2*h

V = (1/3) * pi * (10) ^2 * (1.528) = 160 cm^3

Therefore your answer is C.