Some info about the surface area and volume of the two similar solids has been given. Find the missing value.  Solid 1 SA=54 m² V=648 m³ Solid 2 SA= ? V=8232 m³

4 Answers

sciencesolve's profile pic

sciencesolve | Teacher | (Level 3) Educator Emeritus

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You need to use the definition of similar solids to evaluate the missing value of surface area of solid 2, hence, since the corresponding dimensions of similar solids are proportional, yields:

`V_2/V_1 = (SA_2)/(SA_1)`

`V_1,V_2` represent the volumes of similar solids

`SA_1,SA_2`  represent the surface areas of similar solids

Repacing the values provided by the problem in equality, yields:

`8232/648 = (SA_2)/54 =>(SA_2) = 54*8232/648 => (SA_2) = 686 m^2`

Hence, evaluating the missing value of surfce area of solid 2, under the given conditions, yields `SA_2 = 686 m^2` .

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llltkl | College Teacher | (Level 3) Valedictorian

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For solid 1:

Surface area=`54m^2`


` `

`For solid 2:`

`Surface area=?`


`Volume ratio of solid1:solid2 = 648:8232`

`Since Volume is a function of the cube of the dimensions,`

` ``The ratio of their sides = root(3)(648)/root(3)(8232)`


`Since surface area is a function of the square of the sides,`

`(surface area of solid1)/(surface area of solid2)=8.6534^2/20.1914^2`

`or (54)/(surface area of solid2)=74.88/407.69`

`or surface area of solid2=(54 * 407.69)/74.88`` `


Hence, the surface area of  solid 2 =`294m^2~~`

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pramodpandey | College Teacher | (Level 3) Valedictorian

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The surface-area-to-volume ratio is calculated by dividing the surface area by the volume of any object. If you know the formula for the surface area and the volume of an object, then simply compute (surface area) / (volume) to calculate the surface-area-to-volume ratio. The actual surface-area-to-volume ratio of any object depends upon that object's shape and geometry. Thus it is purely inapproprite

to simplify every things.In my opinion answer  1 and 2 are not correct.

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pramodpandey | College Teacher | (Level 3) Valedictorian

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These are not saying about regular solid. You do not know exact shape of the solid.

so we can not draw any conclusion.