Math, asked by shashisaini1691, 1 year ago

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

Answered by santy2
6

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

Larger Cylinder = 2 × 2.5 = 5cm

Smaller cylinder = 1.5 × 2 = 3cm

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