A cylinder has a radius of 8 centimeters and a height of 12 centimeters. A smaller cylinder has linear dimensions that are one-fourth the dimensions of the larger cylinder. Compare the surface area of the smaller cylinder to the surface area of the larger cylinder.

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biernaldo biernaldo · Answer 1 · 2020-04-04T17:20:34+02:00

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Favouredlyf Favouredlyf · Answer 2 · 2020-04-04T17:49:07+02:00

Answer: the surface area of the larger cylinder is 16 times that of the smaller cylinder.

Step-by-step explanation:

The formula for determining the total surface area of a cylinder is expressed as

Total surface area = 2πr² + 2πrh

Where

r represents the radius of the cylinder.

h represents the height of the cylinder.

π is a constant

Considering the larger cylinder,

radius = 8 cm

Height = 12 cm

Therefore,

Total surface area = (2 × π × 8²) + (2 × π × 8 × 12)

= 128π + 192π = 320π

Considering the smaller cylinder,

Total surface area = 56π

radius = 8/4 = 2cm

Height = 12/4 = 3 cm

Therefore,

Total surface area = (2 × π × 2²) + (2 × π × 2 × 3)

= 8π + 12π = 20π

Ratio of the surface area of the larger cylinder to the smaller cylinder is

320π/20π = 16