Metal cylindrical disc of base radius 20 cm in height 7 cm is melted and recast into a cylindrical lock of base radius 14 cm find the length of cylindrical block also find the ratio when the total surface area of the cylinder is to the block

Step-by-step explanation:

The initial metal cylindrical disc has a base radius of 20 cm and height of 7 cm.

The formula for determining the volume if a cylinder is expressed as

Area = πr^2 h

Where

π is a constant whose value is 3.14

r represents radius of the cylinder.

h represents height of the cylinder.

Volume of the metal cylindrical disc

= π × 20^2 × 7 = 2800π cm^3

The metal cylindrical disc is melted and recast into a cylindrical lock of base radius 14 cm

Volume of the cylindrical lock would also be 8792 cm^3. Therefore,

2800π = π × 14^2 × l

l = 2800π/196π = 14.29 cm

Formula for determining total surface area of a cylinder is expressed as

2πrh + 2πr^2

Total surface area of the metal cylindrical disc would be

(2 × π × 20 × 7) + (2 × π × 20^2)

280π + 800π = 1080π cm^2

Total surface area of the cylindrical block would be

(2 × π × 14 × 14.29) + (2 × π × 14^2)

400.12π + 392π = 792.12 cm^2

The ratio of the total surface area of the cylinder to the block would be

1080/792.12 = 1.36

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