# Find the total surface area of a cone, if its slant height is $21 \mathrm{~m}$ and diameter of its base is $24 \mathrm{~m}$.

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Given:

The slant height of a cone is $21\ m$ and the diameter of its base is $24\ m$.

To do:

We have to find the total surface area of the cone.

Solution:

Slant height of the cone $(l) = 21\ m$

Diameter of the base $= 24\ m$

This implies,

Radius $(r) = \frac{24}{2}$

$=12\ m$

Therefore,

The total surface area of the cone $= \pi r(l + r)$

$=\frac{22}{7} \times 12(21+12)$

$=\frac{22}{7} \times 12 \times 33$

$=\frac{8712}{7}$

$=1244.57 \mathrm{~m}^{2}$

Hence,

The total surface area of the cone is $1244.57 \mathrm{~m}^{2}$.

Updated on 10-Oct-2022 13:46:36