Work out the radius of each cylinder below
Problem 1 :
Solution :
By observing the figure,
Radius r = ?
Height h = 8 cm
Surface area A = 18π cm^{2}
Surface area A= 2πr(h + r)
18π = 2πr(8 + r)
Divide each side by 2π.
18π/2π = (2πr(8 + r))/2π
9 = r(8 + r)
9 = 8r + r^{2}
r^{2} + 8r – 9 = 0
(r + 9)(r - 1) = 0
r = 1 cm
Problem 2 :
Solution :
By observing the figure,
Radius r = ?
Height h = 7 cm
Surface area A = 36π cm^{2}
Surface area A= 2πr(h + r)
36π = 2πr(7 + r)
Divide each side by 2π.
36π/2π = (2πr(7 + r))/2π
18 = r(7 + r)
18 = 7r + r^{2}
r^{2} + 7r – 18 = 0
r = 2 cm
Problem 3 :
The radius and height of a cylinder are 5 : 7 and volume is 550 cm^{3}. Find the total surface area.
Solution :
Radius = 5x and height = 7x
Volume of cylinder = 550 cm^{3}
πr^{2}h = 550
Radius = 5(1) ==> 5
height = 7(1) ==> 7
Total surface area of cylinder = 2πr(h + r)
= 2π . 5(7 + 5)
= 10π (12)
= 120π cm^{2}
Problem 4 :
The circumference of the base of a right circular cylinder is 220 cm. If the height of the cylinder is is 2 m, find the total surface area of cylinder.
Solution :
Circumference of the base of cylinder = 220 cm
2πr = 220
2. (22/7) . r = 220
r = 220 . (7/22) . (1/2)
r = 35
h = 2 m
Curved surface area of cylinder = 2πr(h + r)
Problem 5 :
A roller of diameter 70 cm and the length 2 m is rolling on the ground. What is the area by the roller in 50 revolutions ?
Solution :
Radius of the roller = 70 cm
height of the roller = 2 m ==> 200 cm
Area covered in revolution = 2πrh
= 2 . (22/7) . 70 . 200
= 88000 cm^{2}
= 8.8 m^{2}
Area covered in 50 revolution = 8.8 (50)
= 440 m^{2}
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM