Question

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

Answer 1

Scale factor = (1728/343)^(1/3) = 12/7 Let the surface area of the smaller solid be A, then: A * (12/7)^2 = 576 So A = 196

Answer 2

Answer:

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 = $\frac{343}{1728}$

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 = $\sqrt[3]{\frac{343}{1728} }=\frac{7}{12}$

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 = $(\frac{7}{12})^{2}$ = (Surface area of smaller solid)/(surface area of larger solid)

Area of larger solid = 576 m²

$(\frac{7}{12})^{2}=\frac{S}{576}$

$S=\frac{49}{144}.(576)=(49).(4)=196$

Surface area of of the smaller solid = 196 m²

Option A. is the answer.