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Find the total surface area of a cone, if its slant height is $21\ m$ and diameter of its base is $24\ m$.
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 $1244.57 \mathrm{~m}^{2}$.
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