Question

7. A tent is in the shape of a cylinder surmounted by a conical top. If the height and
diameter of the cylindrical part are 2.1 m and 4 m respectively, and the slant height of the
top is 2.8 m, find the area of the canvas used for making the tent. Also, find the cost of
the canvas of the tent at the rate of 500 per m². (Note that the base of the tent will not
be covered with canvas.)​

Answer 1

Given :-

Diameter of the tent = 4 m

Slant height of the cone = 2.8 m

Height of the cylinder = 2.1 m

The cost of the canvas of the tent per m² = Rs. 500

To Find :-

The area of the canvas used for making the tent.

The cost of the canvas of the tent at the rate of ₹500 per m²

Analysis :-

The required surface area of tent = surface area of cone + surface area of cylinder

Total cost = surface area × cost per m²

Solution :-

We know that,

• d = Diameter
• l = Slant height
• h = Height
• r = Radius

Given that,

Diameter (d) = 4 m

Slant height (l) = 2.8 m

Height (h) = 2.1 m

Radius = $\sf \dfrac{Diameter}{2}$

Radius = $\sf \dfrac{4}{2} =2 \: m$

So, the required surface area of tent = TSA of cone + TSA of cylinder

$\implies \sf \pi rl+2 \pi rh$

$\implies \sf \pi r(l+2h)$

Taking the value of pi as 22/7 and substituting the values given, we get

$\implies \sf \bigg(\dfrac{22}{7} \bigg) \times 2(2.8+2 \times 2.1)$

$\implies \sf \bigg( \dfrac{44}{7} \bigg)(2.8+4.2)$

$\implies \sf \bigg( \dfrac{44}{7} \bigg) \times 7 = 44 m^{2}$

∴ The cost of the canvas of the tent at the rate of ₹500 per m² = Surface area × cost per m²

Substituting these data,

$\implies \sf 44 \times 500 = Rs. \: 22000$

Therefore, Rs. 22000 will be the total cost of the canvas.

To Note :-

Total Surface area = Curved surface area of cone + Curved surface area of hemisphere = πrl + 2πr²

Rectangular solids and cylinders are somewhat similar because they both have two bases and a height.

Answer 2

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From the question, we know that

The diameter = D = 4 m

l = 2.8 m (slant height)

The radius of the cylinder is equal to the radius of the cylinder

So, r = 4/2 = 2 m

Also, we know the height of the cylinder (h) is 2.1 m

So, the required surface area of the given tent = surface area of the cone (the top) + surface area of the cylinder(the base)

= πrl + 2πrh

= πr (l+2h)

Now, substituting the values and solving it we get the value as 44 m^2

∴ The cost of the canvas at the rate of Rs. 500 per m^2 for the tent will be

= Surface area × cost/ m^2

= 44 × 500

So, Rs. 22000 will be the total cost of the canvas

Hope it's Helpful.....:)