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

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Given:-

• Total surface area of cone is 17776 m²

• The radius of cone is 56 m

$\text{\large\underline{\green{To find:-}}}$

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

$\text{\large\underline{\purple{Solution:-}}}$

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 ❞

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Answer 2

Answer :

➥ The slant height of the cone = 45 m

Given :

➤ Total surface area of the cone = 1777 m³

➤ Radius of the cone = 56 m

To Find :

➤ Slant height of the cone = ?

Solution :

Let ,

The slant height of the cone be "l"

As we know that

$\tt {: \implies T.S.A_{(cone)} = \pi r (l + r)}$

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

$\tt{: \implies 17776 = 22 \times 8(l + 56)}$

$\tt{: \implies 17776 = 176(l + 56)}$

$\tt{: \implies \cancel{\dfrac{17776}{176}} = l + 56}$

$\tt{: \implies 101 = l + 56}$

$\tt{: \implies 101 - 56 = l}$

$\tt{: \implies 45 = l}$

$\bf{: \implies \underline{ \: \: \underline{ \purple{ \: \: l = 45 \: m \: \: }} \: \: }}$

Hence, the slant height of the cone is 45 m.

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Some releted formulae :

⪼ Curved Surface area of Cone = πrl

⪼ Total Surface Area of Cone = πr(l + r)

⪼ Volume of Cone = ⅓πr²h