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Mathematics

Find the volume of a cone whose slant height is 17 cm and radius of base is 8 cm.

Mensuration

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Answer

Given,

Slant height (l) = 17 cm

Radius (r) = 8 cm

Let height of cone be h cm.

We know that,

⇒ l2 = h2 + r2

⇒ 172 = h2 + 82

⇒ 289 = h2 + 64

⇒ h2 = 225

⇒ h = 225\sqrt{225} = 15 cm.

By formula,

Volume of cone = 13πr2h\dfrac{1}{3}πr^2h

=13×227×82×15=22×64×57=70407=1005.71 cm3.= \dfrac{1}{3} \times \dfrac{22}{7} \times 8^2 \times 15 \\[1em] = \dfrac{22 \times 64 \times 5}{7} \\[1em] = \dfrac{7040}{7} \\[1em] = 1005.71 \text{ cm}^3.

Hence, volume of cone = 1005.71 cm3.

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