Question

curved surface area of cone is 20 pi square cm slant height and radius are consecutive natural number then finf volume.​

Answer 1

Answer:

$\red { Volume \:of \: the \:cone }\green {= 16\pi \:cm^{3} }$

Step-by-step explanation:

$Let \: radius \: of \: a \: cone = r \:cm$

$Slant\: height (l) = (r+1) \:cm \\(Given \: r\:and \:l \: are \: consecutive \: natural \: numbers)$

$Curved \: surface \:Area \: of \:a \:cone = 20\pi$

$\implies \pi rl = 20\pi$

$\implies \pi r(r+1) = 20\pi$

$\implies r(r+1) = 20$

$\implies r(r+1) = 4\times (4+1)$

$r = 4 \:cm$

$l = r + 1 = 4 + 1 = 5 \:cm$

$\boxed { \orange { Height(h) = \sqrt{l^{2} - r^{2}}}}$

$\implies h = \sqrt{ 5^{2} - 4^{2}}\\= \sqrt{25-16}\\=\sqrt{9}\\= 3\:cm$

$\pink {Volume} = \frac{1}{3} \pi r^{2}h$

$= \frac{1}{3} \times\pi \times 4^{2} \times 3\\= 16\pi \:cm^{3}$

Therefore.,

$\red { Volume \:of \: the \:cone }\green {= 16\pi \:cm^{3} }$

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