If the diameter of the base of a cone is 18 {cm} and its curved surface area is 424 \frac{2}{7} {cm}^{2}, then its height will be (Take \pi=\frac{22}{7} )

SSC CHSL 19 Apr 2021 Shift 3 Paper

Section: Quantitative Aptitude

Question : 57 of 100

Marks: +1, -0

If the diameter of the base of a cone is

18 {cm}

and its curved surface area is

424 \;{2}/{7} {cm}^{2}

, then its height will be (Take

π=\;{22}/{7}

)

Solution:

Given, diameter of the base of the cone

=18 {cm}

∴ \;\; \;\text " Radius "\;=\;{18}/{2}=9 {cm}

Given, curved surface, area

=424 \;{2}/{7} {cm}^{2}=\;{2970}/{7} {cm}^{2}

⇒ \;\; π r l=\;{2970}/{7}

⇒ \;\; π r × √{h^{2}+r^{2}}=\;{2970}/{7}

⇒ \;\; \;{22}/{7} × 9 × √{h^{2}+(9)^{2}}=\;{2970}/{7}

⇒ \;\; h^{2}+81=(\;{2970}/{7} × \;{7}/{22} × \;{1}/{9})^{2}

=(15)^{2}=225

⇒\;h^{2}=225-81=144

∴ \;h=√{144}=12 {cm}

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