Cone A has a radius of 2 inches and a height of 3 inches. In cone B, the height is the same, but the radius is doubled. Calculate the volume of both cones. Which statement is accurate? A) When the radius is doubled, the resulting volume is half that of the original cone. B) When the radius is doubled, the resulting volume is twice that of the original cone. Eliminate C) When the radius is doubled, the resulting volume is 4 times that of the original cone. D) When the radius is doubled, the resulting volume is 3 times that of the original cone.

Answer: Option C.Step-by-step explanation: Use the formula for calculate the volume of a cone: [tex]V=\frac{1}{3}\pi r^2h[/tex] Where r is the radius and h is the height. Volume of the cone A: [tex]V_A=\frac{1}{3}\pi (2in)^2(3in)=12.56in^3[/tex] Volume of the cone B: If the height of the cone B and the height of the cone A are the same , but the radius of the cone B is doubled, then its radius is: [tex]r_B=2r_A\\r_B=2*2in\\r_B=4in[/tex] Then: [tex]V_B=\frac{1}{3}\pi (4in)^2(3in)=50.26in^3[/tex] Divide [tex]V_B[/tex] by [tex]V_A[/tex]: [tex]\frac{V_B}{V_A}=\frac{50.26in^3}{12.56in^3}=4[/tex] Therefore: When the radius is doubled, the resulting volume is 4 times that of the original cone.