Question

The total surface area of a cone is 792sq.cm. and radius of its base is 14cm.Find the slant height of the cone.(π=22/7)
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Answer 1

S O L U T I O N :

$\underline{\bf{Given\::}}$

• Total surface area of a cone = 792 cm²
• Radius of it's base = 14 cm

$\underline{\bf{Explanation\::}}$

As we know that formula of the total surface area of cone;

$\boxed{\bf{T.S.A = \pi rl + \pi r^{2}\:\:\:(sq.unit)}}$

A/q

$\longrightarrow\tt{T.S.A \:of\:cone = \pi r (l+r)}$

$\longrightarrow\tt{792 = \dfrac{22}{7} \times 14 (l+14)}$

$\longrightarrow\tt{792 = \dfrac{22}{\cancel{7}} \times \cancel{14} (l+14)}$

$\longrightarrow\tt{792 = 22 \times 2 (l+14)}$

$\longrightarrow\tt{792 = 44 (l+14)}$

$\longrightarrow\tt{792 = 44l+616}$

$\longrightarrow\tt{ 44l= 792-616}$

$\longrightarrow\tt{ 44l= 176}$

$\longrightarrow\tt{l= \cancel{176/44}}$

$\longrightarrow\bf{l = 4\:cm}$

Thus,

The slant height of the cone will be 4 cm .