Question

An asteroid has a surface area of 5 m^2. What would its surface area be if its linear dimension is doubled?

Please, explain to me how should I approach this problem because I really don't get it :-(

Answer 1

Assuming that asteroid is spherical in shape, its surface area A= 4*pi*r²

For a sphere , linear dimension is its diameter or radius

Where r is its radius. If r is doubled: new r =r' = 2r

Then Surface area = A' = 4 * pi * r'² = 4 * pi * (2r)² = 4 * 4*pi*r² = 4 * A

or,

New surface area A' = 4 times old Surface area = 4A =4 * 5 = 20 m²

Answer 2

$\hspace{-0.25in}SA \sim r^2 \\ r \to 2r \\ SA \sim r^2 \to (2r)^2 = 4r^2 \\ SA = 5(4) = 20 \, m^2$

Answer 3

surface area=4 x pi x r²=pix(2r)²=pi x d²

A1=pi d1² and A2=pi x d2²

A1/A2=(d1/d2)²

A2=(d2/d1)² A1=(2d1/d1)² x 5=20m²