Question

PLEASE HELP ME OUT i already asked this question but imma ask it again

1). The volume of Solid A is 28 meters cubed and the volume of Solid B is 1,792 meters cubed. If the solids are similar, what is the ratio of the surface area of Solid A to the surface area of Solid B? Use a : or / to write your ratio.


2). The surface area of a triangular pyramid is 1,936 inches squared. If the dimensions are multiplied by 1/4, what will be the new surface area?


Please answer with explanation if possible but i really need this i cant figure it out ty

Answer 1

1) 1/16

2) 121 in²

Explanation:

1) The ratio of volumes of similar shapes is equal to the cube of the ratio of the sides.

V₁/V₂ = (s₁/s₂)³

Similarly, the ratio of the areas equals the square of the ratio of the sides.

A₁/A₂ = (s₁/s₂)²

First, use the volumes to find the ratio of the sides.

28 / 1792 = (s₁/s₂)³

1/64 = (s₁/s₂)³

s₁/s₂ = 1/4

Now find the ratio of the areas.

A₁/A₂ = (1/4)²

A₁/A₂ = 1/16

2) A₁/A₂ = (s₁/s₂)²

If s₁ = s₂/4, and A₂ = 1936:

A₁ / 1936 = (1/4)²

A₁ / 1936 = 1/16

A₁ = 1936 / 16

A₁ = 121 in²