The base of a conical tent is of area $616$ sq. cm. A $48$ cm long vertical pole is placed at its centre so that it touches the roof of the tent. How much canvas is needed to make the tent if the base is also covered with canvas?

$2816 c m^{2}$

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$2861 c m^{2}$

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$2618 c m^{2}$

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$2681 c m^{2}$

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Solution

The correct option is A. $2816 c m^{2}$
Here, we need to calculate the total surface area of the cone.
Total surface area of the cone = $π r (l + r)$
$= π r l + π r^{2}$
where $π r^{2}$ is the area of the base of the cone.
Given: $π r^{2} = 616 c m^{2}$
$\Rightarrow \frac{22}{7} \times r^{2} = 616$
$\Rightarrow r^{2} = 616 \times \frac{7}{22} = 196 c m^{2}$
$\Rightarrow r = 14 c m$
Also, $h = 48 c m$
Now, $l = \sqrt{h^{2} + r^{2}}$
$= \sqrt{48^{2} + 14^{2}}$
$= \sqrt{2304 + 196}$
$= \sqrt{2500} = 50 c m$
So, T. S. A of conical tent $= π r l + π r^{2}$
$= \frac{22}{7} \times 14 \times 50 + 616$
$= 2816 c m^{2}$

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The base of a conical tent is of area 616 sq. cm. A 48 cm long vertical pole is placed at its centre so that it touches the roof of the tent. How much canvas is needed to make the tent if the base is also covered with canvas?

The base of a conical tent is of area $616$ sq. cm. A $48$ cm long vertical pole is placed at its centre so that it touches the roof of the tent. How much canvas is needed to make the tent if the base is also covered with canvas?