Question

A circus tent is cylindrical up to a height of 7 m and is in the shape of a cone over it, the diameter of the cylindrical part is 10 m and the total height of the tent is 19 m. Find the cost of making the tent at a cost of 35 per square meter of cloth.
please help me on this and ​

Answer 1

$\bold{\huge{\underline{ Solution }}}$

Given :-

• The circus tent is composed of cylinder and a cone.

• The height and diameter of the cylindrical part are 7m and 10m

• The total height of the circus tent 19m

• The cost of making the tent at a cost of 35 m² cloth.

Let's Begin :-

Here, we have ,

• Cylinder and cone
• The height and diameter of the cylinder are 7m and 10m
• Therefore , radius = 5 m

We know that,

Curved Surface area of the cylinder

$\sf{ = 2{\pi}rh}$

Subsitute the required values,

$\sf{ = 2{\times}3.14{\times}5{\times}7}$

$\sf{ = 6.28 {\times}5{\times}7}$

$\sf{ = 6.28 {\times}35}$

$\bold{ = 219.8m^{2}}$

Thus, The area of the cylinder is 219.8m² .

Now,

•We have to find the area of the cone.

•Here, Base of cone = diameter of the cylinder.

•The height of the cone will be

= Height of the tent - Height of cylinder

$\sf{ = 19 - 7 }$

$\bold{ = 12 m }$

We know that,

Area of cone

$\bold{ = {\pi}rl }$

• Here, l is the slant height.

Slant height of the cone

$\sf{ = \sqrt{ h^{2} + r^{2}} }$

$\sf{ = \sqrt{ (12)^{2} + (5)^{2}} }$

$\sf{ = \sqrt{ 144 + 25}}$

$\sf{ = \sqrt{ 169}}$

$\sf{ = \sqrt{ 13{\times} 13 }}$

$\bold{ = 13 m }$

Thus, The slant height of the cone is 13 m

Subsitute the required values in the above formula

$\sf{ = 3.14 {\times} 5 {\times} 13}$

$\sf{ = 3.14 {\times} 65}$

$\bold{ = 204.1 m^{2}}$

Thus, The area of the cone is 204.1 m² .

Therefore ,

The total area of the circus tent

$\sf{ = 204.1 + 219.8}$

$\bold{ = 423.9m^{2} \: or \: 424 m^{2}}$

Now,

• We have to find the total cost of making the tent.
• The cost for 1 m² = 35

Therefore,

The total cost for making the circus tent

$\sf{ = 424 {\times} 35}$

$\bold{ = 14840}$

Hence, The total cost for making the tent is 14840 .

Answer 2

Given:-

• Diameter of cylinder=10m
• Height of cylinder=7m
• Height of tent=19m

Formalise :-

• Radius of cylinder=r=10/2=5m
• Height=h=7m

TSA of cylinder

• 2πr(h+r)
• 2π(5)(5+7)
• 10π(12)
• 120π
• 376.8m²

For cone

• radius=r=5m
• Height=h=19-7=12m

Find slant height=l

• l²=h²+r²
• l²=12²+5²
• l²=144+25
• l²=169
• l=13m

Now

LSA of cone

• πrl
• π(5)(13)
• 65π
• 204.1m²

Total area of tent

• 204.1+376.8
• 580.9m²

But look at the attachment

• We can't paint the shaded region which is base of cone and a circle

So

area of shaded region

• πr²
• 5²π
• 25π
• 78.5m²

TOTAL area to be painted

• 580.9-78.5
• 502.4m²

Total cost

• 502.4(35)
• $17584