Question

The radius of a cone is 7 cm and area of lateral surface is 176 CM square find the slant height

Answer 1

Answer:

Given :-

• The radius of a cone is 7 cm and area of lateral surface is 176 cm².

To Find :-

• What is the slant height of cone.

Formula Used :-

$\clubsuit$ Lateral Surface Area or LSA of Cone Formula :

$\mapsto \sf\boxed{\bold{\pink{Lateral\: Surface\: Area_{(Cone)} =\: {\pi}rl}}}$

where,

• π = pie (22/7)
• r = Radius
• l = Slant Height

Solution :-

Let,

$\mapsto \sf\bold{Slant\: Height\: of\: Cone =\: l\: cm}$

Given :

$\bigstar\: \rm{\bold{Lateral\: Surface\: Area =\: 176\; cm^2}}$

$\bigstar\: \rm{\bold{Radius =\: 7\: cm}}$

According to the question by using the formula we get,

$\longrightarrow \sf \dfrac{22}{7} \times 7 \times l =\: 176$

$\longrightarrow \sf \dfrac{22}{7} \times 7l =\: 176$

$\longrightarrow \sf 7l =\: \dfrac{176 \times 7}{22}$

$\longrightarrow \sf 7l =\: \dfrac{\cancel{1232}}{\cancel{22}}$

$\longrightarrow \sf 7l =\: 56$

$\longrightarrow \sf l =\: \dfrac{\cancel{56}}{\cancel{7}}$

$\longrightarrow \sf\bold{\red{l =\: 8\: cm}}$

Hence,

$\mapsto \sf\bold{\purple{Slant\: Height\: of\: Cone =\: 8\: cm}}$

$\therefore$ The slant height of cone is 8 cm .

Answer 2

Solution :

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• Radius of the cone : 7 cm

• LSA of the cone : 176 cm² .

Let us assume that the radius of the cone is r .

LSA = πrl ( l is the slant height)

> 22/7 r l = 176

r = 7 cm as mentioned .

> 22l = 176

> l = 8 cm .

Answer : The slant height of the cone is 8 cm .

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