The slant height of a cone is 17 cm and the radius of its base is 15 cm. Find:

(i) the height of the cone

(ii) the volume of the cone

(iii) the total surface area of the cone

Given, slant height, l = 17 cm and radius, r = 15 cm

(i) l² = r² + h²

⇒ h² = l² - r²

⇒ h² = 17² - 15²

⇒ h² = 289 - 225

⇒ h² = 64

⇒ h = $\sqrt{64} = 8 \text{ cm.}$

Hence, height of the cone is 8 cm.

(ii) Volume of cone = $\dfrac{1}{3}$ πr²h

$= \dfrac{1}{3} \times \dfrac{22}{7} \times 15^2 \times 8 \\[1em] = \dfrac{22}{21} \times 225 \times 8 \\[1em] = \dfrac{39600}{21} \\[1em] = 1885.7 \text{ cm}^3$

Hence, volume of the cone is 1885.7 cm³.

(iii) Total surface area = πr(l + r)

$= \dfrac{22}{7} \times 15(17 + 15) \\[1em] = \dfrac{330}{7} \times (32) \\[1em] = \dfrac{10560}{7} \\[1em] = 1508.6 \text{ cm}^2$

Hence, total surface area of the cone is 1508.6 cm².