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.?
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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.?
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Given:-
[tex]\text{\large\underline{\green{To find:-}}}[/tex]
What is the slant height (l) of the cone ?
[tex]\text{\large\underline{\purple{Solution:-}}}[/tex]
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:-
[tex]\large{\boxed{\bf{\star \: AREA = \pi r (l+r) \: \star}}}[/tex]
According to question:-
On putting the given values in the formula, we get
Take π = 22/7
[tex]\rm{\hookrightarrow 17776 = \dfrac{22}{\cancel{7}} \times \cancel{56} (l + 56)}[/tex]
[tex]\rm{\hookrightarrow 17776 = 22 \times (8l + 448) }[/tex]
[tex]\rm{\hookrightarrow \cancel\dfrac{17776}{22} = 8l + 448 }[/tex]
[tex]\rm{\hookrightarrow 808 = 8l + 448 }[/tex]
[tex]\rm{\hookrightarrow 808-448 = 8l }[/tex]
[tex]\rm{\hookrightarrow 360 = 8l }[/tex]
[tex]\rm{\hookrightarrow \cancel\dfrac{360}{8} = l }[/tex]
[tex]\bf{\hookrightarrow 45 = l}[/tex]
Slant height = l = 45 m
❝ Hence, the slant height (l) of the cone is 45 m ❞
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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
[tex] \tt {: \implies T.S.A_{(cone)} = \pi r (l + r)}[/tex]
[tex] \tt{: \implies 17776 = \dfrac{22}{ \cancel{7}} \times \cancel{56}(l + 56) }[/tex]
[tex] \tt{: \implies 17776 = 22 \times 8(l + 56)}[/tex]
[tex] \tt{: \implies 17776 = 176(l + 56)}[/tex]
[tex] \tt{: \implies \cancel{\dfrac{17776}{176}} = l + 56}[/tex]
[tex] \tt{: \implies 101 = l + 56}[/tex]
[tex] \tt{: \implies 101 - 56 = l}[/tex]
[tex] \tt{: \implies 45 = l}[/tex]
[tex] \bf{: \implies \underline{ \: \: \underline{ \purple{ \: \: l = 45 \: m \: \: }} \: \: }}[/tex]
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