The volumes of two similar solids are 1,728 m^3 and 343 m^3. the surface area of the larger solid is 576 m^2. what is the surface area of the smaller solid? a. 196 m^2 b. 76m^2 c. 1,372m^2 d. 392 m^2

Option a. 196 m²

Step-by-step explanation:

Volumes of two similar solids are 1728 m³ and 343 m³

So the ratio of these volumes =

Now we know volume is a three dimensional unit so we find the cube root of the ratio of the volumes to find the ratio of sides.

Scale factor =

Now we know area of solids is a two dimensional unit so we will square the scale factor and this will be the ratio of area

(Scale factor)² = = (Surface area of smaller solid)/(surface area of larger solid)

Area of larger solid = 576 m²

Surface area of of the smaller solid = 196 m²

Option A. is the answer.

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below: