Question

A cylinder has a surface area of 224in 2. If all dimensions of this cylinder are multipled by 1/4 to crate a new cylinder what will be the surface area of the new cylinder

Answer 1

`\boxed{\text{14 in}^(2)}`

Explanation:

The scale factor (C) is the ratio of corresponding parts of the two cylinders.

The ratio of the areas is the square of the scale factor.

`(A_(1))/( A_(2)) = C^(2)\\ \\(224)/( A_(2)) = \left ((1)/((1)/(4)) \right )^(2)\\\\(224)/( A_(2))= 16\\A_(2) = (224)/(16\\\\)`

A₂ = 14 in²

The surface area of the new cylinder will be
`\boxed{\textbf{14 in}^(2)}`.