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The total surface area of a cone is $704 {cm}^{2}$ and radius of its base is $7 cm$ . Find the slant height of the cone. $(π = \frac{22}{7})$

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25 cm

30 cm

20 cm

15 cm

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) = 7 cm

.
And, surface area of the cone

(S) = 704 {cm}^{2}

\Rightarrow π r \times (l + r) = 704

\Rightarrow \frac{22}{7} \times 7 \times (l + 7) = 704

\Rightarrow 22 (l + 7) = 704

\Rightarrow 22 l + 154 = 704

\Rightarrow 22 l = 704 - 154

\Rightarrow 22 l = 550

\Rightarrow l = \frac{550}{22}

\Rightarrow l = 25 cm

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