Question

What is the slant height of cone if the total surface area of cone is 17776 meter cube and the radius of cone is 56 m.?​

Answer 1

GIVEN:

$\longrightarrow\sf{Total\: surface\: area \: of \: cone = 17776\: m^3 }$

$\longrightarrow\textsf{Radius of the cone = 56 cm}$

TO FIND:

$\longrightarrow\sf\red{Slant \: height \: of \: the \: cone}⟶$

SOLUTION:

Let the slant height be "l"

We know that,

$\longmapsto\underline{\boxed{\sf\green{Total\: surface\: area \: of \: cone = \pi r [ r + l ] }}}⟼Totalsurfaceareaofcone=πr[r+l]$

Substitute the values.

$\implies\sf 17776 = \pi r [ r + l ]⟹17776=πr[r+l]$

$\implies\sf 22/7 \times 56 [ 56 + l ] = 17776⟹22/7×56[56+l]$

$\implies\sf 22 \times 8 [ 56 + l ] = 17776⟹22×8[56+l]$

$\implies\sf 176 [ 56 + l ] = 17776⟹176[56+l]$

$\implies\sf 56 + l = \dfrac{17776}{176}$

$\implies\sf 56 + l = 101$

$\implies\sf l = 101 - 56$

$\implies\sf l = 45$

$\therefore\underline\textsf{ The slant height of the cone is 45m.}$

Answer 2

Given :

• TSA of cone = 17776 m²
• Radius of cone = 56 m

To Find :

• Slant height $\sf (\ell)$ of the cone = ?

Solution :

We know that,

$\large \underline{\boxed{\bf{TSA = \pi r (l+r)}}}$

By substituting values, and take π = $\sf \dfrac{22}{7}$

$\sf : \implies 17776 = \dfrac{22}{\cancel{7}} \times \cancel{56} ( \ell + 56)$

$\sf : \implies 17776 = 22 \times (8 \ell + 448)$

$\sf : \implies \cancel\dfrac{17776}{22} = 8 \ell + 448$

$\sf : \implies 808 = 8 \ell + 448$

$\sf : \implies 808-448 = 8 \ell$

$\sf : \implies 360 = 8 \ell$

$\sf : \implies \cancel\dfrac{360}{8} = \ell$

$\sf : \implies 45 = \ell$

Hence, Slant height $\sf (\ell)$ of cone = 45 m.