Circular cylinder, 14cm long is 88cm² if the volume of the metal used in making the cylinder is 176cm³. Find the outer and inner diameter of the cylinder
Answers
Answer:
Step-by-step explanation:
The difference between the surface area of the inner cylinder and the outer cylinder is 88cm².
From this we can get the thickness of the cylinder.
Curved Surface area = 2πrh
Doing the substitution we have :
88 = 2 × 22/7 × 14 × r
88 = 88r
r = 1
This implies that the thickness of the metal cylinder is 1 cm.
Now let the radius of the inner cylinder be x.
the radius of the outer cylinder will be :
(x + 1)
The volume of a cylinder = πr²h
volume of inner cylinder = πx² × 14 = 14πx²
Volume of outer cylinder = 14π(x + 1)²
= 14π(x² + 2x + 1)
Volume of the metal used = Difference between the volume of the outer and inner cylinders
This is given by :
(14πx² + 28πx + 14π) - 14πx² = 28πx + 14π
This equals to 176.
28πx + 14π = 176
π = 22/7
88x + 44 = 176
88x = 176 - 44
88x = 132
x = 132/88
x = 1.5
The radius of the larger cylinder is thus :
1.5 + 1 = 2.5 cm
diameter = radius × 2