Question

The curved surface area of a cone is 4070 cm² and its diameter is 70 cm. What is its slant height?

Answer 1

Csa of cone = pi.r.l

pi.35.l = 4070

22/7 . 35 . l = 4070

l = 4070 / 110

l = 37 cm

Answer 2

$\bf{\underline{\underline \blue{Solution:-}}}$

AnswEr:

• Slant height of the cone = 37 Cm

Given:

• The curved surface area of a cone is 4070 cm² and its diameter is 70 cm.

Need To Find:

• Slant height of the cone = ?

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

Formula used here:

$\bigstar \: \boxed{ \sf \: Radius\: of \:cone = \frac{Diameter}{2 } }$

Putting the values we get:

$\longrightarrow \sf \green {Radius\:of\:cone = \dfrac{\cancel{70}}{\cancel{2}}\:}$

$\longrightarrow \sf \green { Radius\:of\:cone = 35\:Cm}$

ThereFore:

• The radius of cone is 35 Cm.

Now, Again Formula Used Here:

$\bigstar \: \boxed{ \sf \: Curved \:surface \:area \:of \:a\: cone\: is = \pi rl }$

Putting the values according to the given formula:

$\longrightarrow \sf \pink {\pi rl = 4070}$

$\longrightarrow \sf \pink {\dfrac{22}{\cancel7}\times \cancel{35}\times L = 4070}$

$\longrightarrow \sf \pink {22 \times 5 L = 4070}$

$\longrightarrow \sf \pink {110 \:L}$

$\longrightarrow \sf \pink {L = \dfrac{\cancel{4070}}{\cancel{110}} \:}$

$\longrightarrow \sf \pink { L = 37\:cm}$

ThereFore:

• Slant height of the cone is 37 Cm.

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