Answer to Question #114340 in Geometry for James Brown

Question

Assume Cylinder A and Cone B are the same height and the bases have the same radius. If A has a volume of 18π cm3, what is the volume of B? (round to nearest whole number)

Answer 1

Let $V_A$ be the volume of cylinder, $V_B$ be the volume of cone. We know that $V_A = \pi r_A^2h_A$, $V_B = \pi r_B^2h_B/3$ , where $h$ is the height and $r$ is the radius. $h_A = h_B$ and $r_A = r_B$ by conditions of the problem. We have

$V_B = \pi r_b^2h_b/3 = \pi r_A^2h_A/3 = V_A/3= \\=18\pi/3=6\pi= 18.84cm^3 \approx 19 cm^3.$

Answer: $19cm^3$.