Question

The surface areas of two similar solids are 1,008^cm and 1,372 cm^ The volume of the larger solid is 1,801cm ^3. Find the volume of the smaller solid. Round your answer to the nearest hundredth. A. 252.15cm^3 B. 1,134.16cm ^3 C. 1,323.18cm ^3 D. 1,372.19cm ^3

Answer 1

the ratio of the volumes of the smaller to larger solid equals the ratio of the surface area to the power 3/2.

= 1008^(3/2) : 1372^(3/2) =   32003 :  50820

So volume of the smaller solid
= 1801 * 32003  / 50820  = 1134 cm^3

It's  B

Answer 2

Answer:

Option B. 1134.16 cm³

Step-by-step explanation:

The surface area of two similar solids are 1,008 cm² and 1372 cm²

Since surface area is a two dimensional unit or surface area is the multiplication of two dimensions.

Ratio of the sides of the solids will be

Ratio of sides = $\sqrt{\frac{1372}{1008} }$

                       $=\sqrt{\frac{4\times 343}{4\times 252}}$

                       $=\sqrt{\frac{343}{252}}$$=\sqrt{1.3611}$ = 1.167

Now ratio of volume of the solids will be cube of the sides.

$\frac{\text{Volume of larger solid}}{\text{Volume of smaller solid}}=(\frac{1.167}{1} )^{3}$ = $\frac{1801}{V}$

By cross multiplication

V(1.167)³ = 1801

V = $\frac{1801}{(1.167)^{3}}=\frac{1801}{1.588}$ = 1134.16 cm³

Option B. 1134.16 cm³ is the answer.