Answer:
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