Mathematics

Find the total surface area of a cone, if its slant height is 21 m and diameter of its base is 24 m.

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Given,

Diameter of cone (d) = 24 m

Radius of cone (r) = $\dfrac{\text{Diameter}}{2} = \dfrac{24}{2}$ = 12 m

Slant height of the cone (l) = 21 m

Total surface area of the cone = Curved surface area of cone + area of the base

By formula,

Total surface area of the cone (T.S.A.) = πrl + πr² = πr(l + r)

Susbtituting values we get :

$= \dfrac{22}{7} \times 12 \times (12 + 21) \\[1em] = \dfrac{22}{7} \times 12 \times 33 \\[1em] = \dfrac{8712}{7} \\[1em] = 1244.57 \text{ m}^2$

Hence, total surface area of the cone = 1244.57 m².

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