What is cone ?
A cone is a three-dimensional shape in geometry that narrows smoothly from a flat base (usually circular base) to a point(which forms an axis to the center of base) called the apex or vertex.
To find lateral surface area and total surface area of cone, we use the formulas given below.
Lateral surface area = πrl
Total surface area = πrl + πr^{2}
= πr(l + r)
l = √r^{2} + h^{2}
Here r = radius, l = slant height
Problem 1 :
Solution :
Total surface area = 800π
πr(l + r) = 800π
Dividing by π on both sides, we get
r(l + r) = 800 ----(1)
From the given figure, r = 16 cm and h = x
l = √(16^{2} + x^{2})
Applying the value of l in (1), we get
16(√(16^{2} + x^{2}) + 16) = 800
(√(16^{2} + x^{2}) + 16) = 50
√(16^{2} + x^{2}) = 50 - 16
√(16^{2} + x^{2}) = 34
Take square on both sides.
256 + x^{2} = (34)^{2}
256 + x^{2} = 1156
x^{2} = 1156 - 256
x^{2} = 900
x = 30
Problem 2 :
Solution :
Total surface area = 750
πr(l + r) = 750
Here π = 3.14, r = 6
3.14(6)(l + 6) = 750
l + 6 = 750/18.84
l + 6 = 39.80
l = √(6^{2} + x^{2})
Applying the value of l, we get
√(6^{2} + x^{2}) + 6 = 39.80
√(6^{2} + x^{2}) = 33.80
Take square on both sides.
36 + x^{2} = (33.80)^{2}
36 + x^{2} = 1142.44
x^{2} = 1142.44 - 36
x^{2} = 1106.44
x = 33.26
Problem 3 :
Find what length of canvas 3/4 m wide is required to make a conical tent 8 m in diameter and 3 m in high.
Solution :
Required quantity of canvas = Curved surface area of tent
length x width = πrl
Diameter = 8 m, r = 4 m, height = 3 m
l = √(r^{2} + h^{2})
slant height (l) = √(4^{2} + 3^{2})
l = √25
l = 5
length x (3/4) = 3.14(4)(5)
length x (3/4) = 62.8
length = 62.8(4/3)
length = 83.73
So, the required length of the canvas is 83.73 m.
May 21, 24 08:51 PM
May 21, 24 08:51 AM
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