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

Option B. 1134.16 cm³

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{(1372)/(1008) }`

`=\sqrt{(4* 343)/(4* 252)}`

`=\sqrt{(343)/(252)}`
`=√(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}}=((1.167)/(1) )^(3)` =
`(1801)/(V)`

By cross multiplication

V(1.167)³ = 1801

V =
`(1801)/((1.167)^(3))=(1801)/(1.588)` = 1134.16 cm³

Option B. 1134.16 cm³ is the answer.