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

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 = $\sqrt{225}$ = 15 cm.

By formula,

Volume of cone = $\dfrac{1}{3}πr^2h$

$= \dfrac{1}{3} \times \dfrac{22}{7} \times 8^2 \times 15 \\[1em] = \dfrac{22 \times 64 \times 5}{7} \\[1em] = \dfrac{7040}{7} \\[1em] = 1005.71 \text{ cm}^3.$

Hence, volume of cone = 1005.71 cm³.