Question

The volumes of two similar figures are given. The surface area of the smaller figure is given. find the surface area of the larger figure

V=2875 m^3
V = 1472 m^3
S.A. = 928 m^2
The surface area of the larger figure is [blank] m^2

Answer 1

Explanation:

the surface area of a figure is always the result of a combination of multiplication(s) of 2 dimensions (side lengths).

and the volume of 3 dimensions (side lengths).

"similar figures" means that they share the same angles. and that there is one scaling factor that applies to all sides (and all other lines like heights).

so, no matter what sides are used to calculate the surface areas and the volumes, it is the same scaling factor used for each of them.

in a multiplication of 2 sides (for the area) the scaling factor is therefore applied twice and hence squared, in a multiplication of 3 sides it is applied 3 times and therefore cubed.

let's call the scaling factor f.

1472 × f³ = 2875

and then

928 × f² = large S.A.

let's use the first to get f :

1472 × f³ = 2875

f³ = 2875 / 1472 = (125 × 23) / (64 × 23) = 125/64

f = 5/4

f² = (5/4)² = 5²/4² = 25/16

large S.A. = 928 × 25/16 = 58 × 25 = 1450 m²