Respuesta :
Answer:
Answer is circumference =32.64
Step-by-step explanation:
[tex]given \\ volume \: of \: cone \: = 90\pi \: {cm}^{3} \\ and \: height = 10 \: cm \: \\ to \: find: circumference \\ by \: the \: given \: data \\ volume \: of \: cone = 90\pi \\ \frac{1}{3} \pi {r}^{2} h = 90\pi \\ cancelling \: \pi \: which \: is \: common \: \\ we \: get \\ \frac{1}{3 } {r}^{2} h = 90 \\ we \: know \: that \: h = 10 \\ on \: substituting \: we \: get \\ \frac{1}{3} {r}^{2} \times 10 = 90 \\ dividing \: by \: 10 \: on \: both \: sides \: we \: get \\ \frac{1}{3} {r}^{2} = 9 \\ {r }^{2} = 27 \\ r = 3 \sqrt{3} \\ we \: know \: that \: circumference \: = 2\pi \: r \\ = 2 \times \frac{22}{7} \times 3 \sqrt{3} \\ on \: solving \: the \: above \: mentioned \: we \: get \\ \\ \: = 32.64[/tex]
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