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A conical tent requires 264{{m}^{2}} of canvas. If the slant height is 12 m, find the vertical height of the cone
Class 10 | Frank | ICSE | Maths | Mensuration II
A conical tent requires 264{{m}^{2}} of canvas. If the slant height is 12 m, find the vertical height of the cone

Solution: –

According to the given question,

The curved surface area of the tent is 264{{m}^{2}}.

The slant height of tent is 12 m.

Then, \pi rl=264

\frac{22}{7}\times r\times 12=264

Now, by cross multiplication we get,

r=\frac{\left( 264\times 7 \right)}{\left( 22\times 12 \right)}

r=7m

Let us consider h be the vertical height,

Then,

{{l}^{2}}={{r}^{2}}+{{h}^{2}}

h=\sqrt{\left( {{l}^{2}}-{{r}^{2}} \right)}

h=\sqrt{\left( {{12}^{2}}-{{7}^{2}} \right)}

h=\sqrt{\left( 144-49 \right)}

h=\sqrt{\left( 95 \right)}

h=9.75m.

Therefore, the vertical height of cone is 9.75m.

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