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The total surface area of a conical tent is $920 m^{2}$ and its radius $14 m$ . Find its slant height (Round off your answer to the nearest whole number).

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7 m

25 m

14 m

50 m

answer is A.

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Detailed Solution

Let

l

be the slant height of the cone.
We know the formula for the surface area of a cone i.e

S = πr \times (l + r)

.
Where,

r =

radius of the circle and

l =

slant height of the cone.
Now, it is given that,
Radius of the cone

(r) = 14 m

.
And, surface area of the cone

(S) = 920 m^{2}

\Rightarrow π r \times (l + r) = 920

\Rightarrow \frac{22}{7} \times 14 \times (l + 14) = 920

\Rightarrow 44 (l + 14) = 920

\Rightarrow 44 l + 616 = 920

\Rightarrow 44 l = 920 - 616

\Rightarrow 44 l = 304

\Rightarrow l = \frac{304}{44}

\Rightarrow l = 6.90 m

\Rightarrow l ≃ 7 m

(round off to the nearest whole number)

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