Question

The CSA of a cone is 4070 cm square and it's diameter is 70cm . What is it's slant height

Answer 1

Given :

Curved surface area of cone = 4070cm²

and diameter = 70 cm

To Find :

Slant height of cone

Solution :

Diameter = 70 cm

➝Radius = 35 cm

We know that

Curved surface area of cone = πrl

$\implies\rm{4070=\pi\:rl}$

$\implies\rm{4070=\dfrac{22}{7}\times35\times\:l}$

$\implies\rm{4070=\pi\:rl}$

$\implies\rm{l=\dfrac{4070\times7}{22\times35}}$

$\implies\rm{l=37cm}$

Therefore, The slant height of cone is 37cm

Answer 2

$\red{\huge{\boxed{\sf{Given:}}}}$

The CSA of a cone is 4070 cm square

And it's diameter is 70cm

$\red{\huge{\boxed{\sf{To\ be\ found:}}}}$

The slant height of the cone

The formula for CSA of cone = $\red{\boxed{\boxed{\bf{ \pi rl }}}}$

[∵ In which r = radius and l = slant height of the cone]

Diameter = 70cm

So,

Radius = diameter ÷ 2

Radius = $\bf \frac{70}{2} = 35cm$

Now,

$\implies \bf \pi rl = 4070\\ \\ \bf \implies \frac{22}{7} \times 35 \times l = 4070\\ \\ \bf \implies 22 \times 5 \times l = 4070 \\ \\ \implies \bf 110 \times l = 4070 \\ \\ \implies \bf l = \frac{407 \cancel{0}}{11\cancel{0}} \\ \\ \implies \bf l = 37 cm$

Hence

slant height '$\red{l}$' = 37 cm