Work out the height of each cylinder below.
Problem 1 :
Solution :
Radius r = 3 cm, Height h = ?
Surface area (A) = 84π cm^{2}
Surface area (A) = 2πr (h + r)
84π = 2π(3) (h + 3)
84π = 6π(h + 3)
Divide each side by 6π.
84π/6π = (6π(h + 3))/6π
14 = h + 3
14 – 3 = h
11 cm = h
Problem 2 :
Solution :
Radius r = 10 cm and Height h = ?
Surface area A = 900π cm^{2}
Surface area A= 2πr(h + r)
900π = 2π(10)(h + 10)
900π = 20π(h + 10)
Divide each side by 20π.
900π/20π = (20π(h + 10))/20π
45 = h + 10
45 – 10 = h
35 cm = h
Work out the radius of each cylinder below
Problem 3 :
If a cylinder has a surface area of 100 cm^{2} and its height is 4 times the radius, what is the height of the cylinder ?
Solution :
Surface area of cylinder = 100 cm^{2}
height = 4 (radius)
h = 4r
2πr(h + r) = 100
2πr(4r + r) = 100
2πr(5r) = 100
10πr^{2} = 100
r^{2} = 10/π
r = √(10/π)
height = 4√(10/π)
Problem 4 :
The radius and height of a cylinder are in the ratio 11 : 7. If the curved surface area of cylinder is 121 square cm. Find the radius and height of the cylinder.
Solution :
Radius of the cylinder = 11x and height of the cylinder = 7x
Surface area of cylinder = 121
2πrh = 121
2π 11x 7x = 121
Problem 5 :
The lateral surface area of a right circular cylinder of radius 3 cm is 94.2 cm^{2}. The height of the cylinder is ?
Solution :
Lateral surface area of cylinder = 94.2 cm^{2}
2πrh = 94.2
2 x 3.14 x 3 x h = 94.2
h = 94.2/18.84
h = 5
So, height of the cylinder is 5 cm.
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