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:

• Total surface area of cone is 17776 m²
• The radius of cone is 56 m

TO FIND:

• What is the slant height (l) of the cone ?

SOLUTION:

We have given that, the total surface area of cone is 17776 meter² and the radius of cone is 56 m.

We know that the formula for finding the total surface area of the cone is:-

$\large{\boxed{\bf{\star \: AREA = \pi r (l+r) \: \star}}}$

According to question:-

On putting the given values in the formula, we get

Take π = 22/7

$\rm{\hookrightarrow 17776 = \dfrac{22}{\cancel{7}} \times \cancel{56} (l + 56)}$

$\rm{\hookrightarrow 17776 = 22 \times (8l + 448) }$

$\rm{\hookrightarrow \cancel\dfrac{17776}{22} = 8l + 448 }$

$\rm{\hookrightarrow 808 = 8l + 448 }$

$\rm{\hookrightarrow 808-448 = 8l }$

$\rm{\hookrightarrow 360 = 8l }$

$\rm{\hookrightarrow \cancel\dfrac{360}{8} = l }$

$\bf{\hookrightarrow 45 = l}$

• Slant height = l = 45 m

❝ Hence, the slant height (l) of the cone is 45 m ❞

______________________

Answer 2

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,

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

Substitute the values.

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

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

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

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

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

$\implies\sf 56 + l = 101$

$\implies\sf l = 101 - 56$

$\implies\sf l = 45$

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