A sphere with a radius of 6 cm has the same volume as a cone with a height of 6 cm. What is the radius of the cone?A) 2 cm B) 4 cm C) 8 cm D) 12 cm

D) 12 cm is the right answerStep-by-step explanation:Given[tex]Radius\ of\ sphere = r_s = 6\ cm\\Height\ of\ cone = h = 6 cm\\[/tex]As the volumes of cone and sphere are same[tex]V_s = V_c\\\frac{4\pi {r_s}^3}{3} = \frac{\pi {r_c}^2h}{3}[/tex]Putting the known values[tex]\frac{4\pi {6}^3}{3} = \frac{\pi {r_c}^2*(6)}{3}[/tex]Dividing both sides by pi[tex]\frac{4\pi {(6)}^3}{3\pi } = \frac{\pi {r_c}^2*(6)}{3\pi }\\\frac{4*{(6)}^3}{3} = \frac{{r_c}^2*(6)}{3}[/tex]Multiplying both sides by 3[tex]4*(6)^3 = 6{r_c}^2\\{r_c}^2 = \frac{4*(6)^3}{6}\\{r_c}^2 = 4 * 6^2\\{r_c}^2 = 144[/tex]Taking Square root on both sides[tex]\sqrt{{r_c}^2}=\sqrt{144}\\r_c = 12\ cm[/tex]Hence,D) 12 cm is the right answerKeywords: Volumes, areasLearn more about volumes at:brainly.com/question/2367554brainly.com/question/2670657#LearnwithBrainly