D) 12 cm is the right answer
Step-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 answer
Keywords: Volumes, areas
Learn more about volumes at:
- brainly.com/question/2367554
- brainly.com/question/2670657
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