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)
Solution:
The figure of the tent below can be created as per the given information
From the above figure, it can be seen that the diameter of the cylindrical part is equal to the diameter of the conical part as the cylindrical part is surmounted by the conical part.
As it's given that the base of the tent will not be covered by the canvas then the base of the cylindrical part of the tent is not included in the area of the canvas required.
The surface of the tent includes the curved surface of the cylindrical part and the curved surface of the conical part only.
The area of the canvas used for making the tent is the surface area of the tent.
Area of the canvas used = CSA of the cylindrical part + CSA of the conical part
We will find the area of the canvas by using formulae;
CSA of the cone = πrl, where r and l are the radius and slant height of the cone respectively.
CSA of the cylinder = 2πrh, where r and h are the radius and height of the cylinder respectively.
Cost of the canvas of the tent = Area of the canvas × Rate of the canvas
Height of the cylinder, h = 2.1 m
Diameter of the cylinder, d = 4 m
Radius of the cylinder, r = d/2 = 4/2 m = 2m
Radius of the cone, r = 2 m
Slant height of the cone, l = 2.8 m
Area of the canvas used = CSA of the cylindrical part + CSA of the conical part
= 2πrh + πrl
= πr (2h + l)
= 22/7 × 2 × (2 × 2.1 + 2.8 m)
= 44/7 × 7
= 44 m2
Cost of the canvas of the tent at = ₹ 500 per m2
Thus, total cost of the canvas of the tent = Area of the canvas × Rate of the canvas
= 44 m2 × ₹ 500 per m2
= ₹ 22000
Thus, the area of the canvas used for making the cylindrical tent is 44 m2 and the cost of the canvas is ₹ 22000.
☛ Check: NCERT Solutions for Class 10 Maths Chapter 13
Video Solution:
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)
NCERT Solutions Class 10 Maths Chapter 13 Exercise 13.1 Question 7
Summary:
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. If the cost of the canvas of the tent is at the rate of ₹ 500 per m2, the area of the canvas used for making the cylindrical tent surrounded by a conical top and the cost of the canvas of the tent are 44 m2 and ₹ 22000 respectively.
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