Find the volume and the total surface area of a cone having slant height 17 cm and base diameter 30 cm. Take π = 3.14

Radius of cone = $\dfrac{30}{2}$ = 15 cm.

l = $\sqrt{r^2 + h^2}$

Putting values we get,

$\Rightarrow 17 = \sqrt{15^2 + h^2} \\[1em] \Rightarrow 17^2 = 15^2 + h^2 \\[1em] \Rightarrow 289 = 225 + h^2 \\[1em] \Rightarrow h^2 = 289 - 225 \\[1em] \Rightarrow h^2 = 64 \\[1em] \Rightarrow h = \sqrt{64} = 8 \text{ cm}.$

Volume of cone (V) = $\dfrac{1}{3}πr^2h$

Putting values we get,

$V = \dfrac{1}{3} \times 3.14 \times 15^2 \times 8 \\[1em] = \dfrac{3.14 \times 225 \times 8}{3} \\[1em] = 1884 \text{ cm}^3$

Total surface area of cone (S) = $πrl + πr^2 = πr(l + r)$

Putting values we get,

$S = 3.14 \times 15 \times (17 + 15) \\[1em] = 3.14 \times 15 \times 32 \\[1em] = 1507.2 \text{ cm}^2$

Hence, the volume of cone = 1884 cm³ and surface area of cone = 1507.2 cm².