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A.$200{m^2}$

B.$250{m^2}$

C.$300{m^2}$

D.$350{m^2}$

Answer

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To find the area of the canvas of the tent, we find the total surface area of the tent. For that, we can divide the tent into a cylinder and a cone and find their area separately.

Consider the cylindrical part of the tent. Its height is given as ${\text{h = 3m}}$. It has diameter${\text{12m}}$. So, the radius is given by,

$r = \dfrac{{diameter}}{2} = \dfrac{{12}}{2} = 6m$

Then curved surface area of the cylinder is given by,

${A_1} = 2\pi rh$

Applying the values of height and radius, we get,

${A_1} = 2 \times 3.14 \times 6 \times 3$

After multiplication, we get,

${A_1} = 113.04{m^2}$

So, the curved surface area of the cylinder is $113.04{m^2}$

Now we consider the conical part. It has slant height of ${\text{l = 10m}}$ and the radius is same as that of the cylinder, i.e. $r = 6m$.

Then the curved surface area of the cone is given by,

${A_2} = \pi rl$

Applying the values of height and radius, we get,

${A_2} = 3.14 \times 6 \times 10$

After multiplication, we get,

${A_2} = 188.4{m^2}$

So, the curved surface area of the conical part is $188.4{m^2}$.

So, the total surface area is given by sum of the area of the cylinder and cone. So, we get,

$A = {A_1} + {A_2}$

On applying the values and adding, we get,

$A = 113.04 + 188.4 = 301.44{m^2}$

Thus, the surface area of the tent is $301.44{m^2}$. So, the area of the canvas is also the same.

Therefore, the area of the canvas just exceeds ${\text{300}}{{\text{m}}^{\text{2}}}$.

So,