The height of a right circular cone is 24 cm and the radius of its base is 7 cm. Calculate :

(i) the slant height of the cone

(ii) the lateral surface area of the cone

(iii) the total surface area of the cone

(iv) the volume of the cone

Given, h = 24 cm and r = 7 cm

(i) Slant height, l = $\sqrt{\text{h}^2 + \text{r}^2} = \sqrt{24^2 + 7^2} = \sqrt{576 + 49} = \sqrt{625} = 25 \text{ cm.}$

Hence, slant height of the cone is 25 cm.

(ii) Lateral surface area = πrl

$= \dfrac{22}{7} \times 7 \times 25 \\[1em] = \dfrac{3850}{7} \\[1em] = 550 \text{ cm}^2$

Hence, lateral surface area of the cone is 550 cm².

(iii) Total surface area = πr(l + r)

$= \dfrac{22}{7} \times 7(25 + 7) \\[1em] = \dfrac{154}{7} \times (32) \\[1em] = \dfrac{4928}{7} \\[1em] = 704 \text{ cm}^2$

Hence, total surface area of the cone is 704 cm².

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

$= \dfrac{1}{3} \times \dfrac{22}{7} \times 7^2 \times 24 \\[1em] = \dfrac{22}{21} \times 49 \times 24 \\[1em] = \dfrac{25872}{21} \\[1em] = 1232 \text{ cm}^3$

Hence, volume of the cone is 1232 cm³.