Question

The volume of two similar solids is 1331 m3 and 729 m3. The surface area of the larger solid is 605 m2.

What is the surface area, in square meters, of the smaller solid?

Answer 1

A)121
B)305
C)405
D)81

Answer 2

Volume of B (Larger Solid) = (Scale Factor)^3 . Volume of A(Smaller Solid)

From this you can find Scale Factor ( Scale Factor is the factor by which the B is larger than A)

Surface Area of B = (Scale Factor)^2 . Surface Are of A

Please go ahead and solve the problem.

Answer 3

@rajee_sam can you please dumb it down im not understanding

Answer 4

when you have two similar solids one is bigger or smaller than the other in dimensions. Do you agree?

Answer 5

yes

Answer 6

the factor that it is larger are smaller is called the scale factor

Answer 7

the dimension of each side I mean

Answer 8

ok

Answer 9

Now if you consider a square that has its side as 2 and another square that has its side a 6 the scale factor is 3 because 2 x 3 = 6

Answer 10

Now if you find the area of the smaller square it will be 2 x 2 = 4

That of the larger square is 6 x 6 = 36

Now if you compare the areas larger one is 9 times bigger than the smaller which is (scale factor )^2 = 3^2 = 9

Answer 11

ok

Answer 12

Hey Isabella, are you ignoring my messages?, just wanna knoe

Answer 13

So Area of Solid B = (Scale Factor)^2 x Area of Solid A

For Area you multiply 2 dimensions so you have (Scale Factor)^2

Now you have to extend this concept to a 3D shape.
the volume is you multiply 3 dimensions. So
Volume of Solid B = (Scale Factor)^3 x Volume of A

Answer 14

okay

Answer 15

now your problem

1331 = (Scale Factor)^3 x 729

\[\frac{ 1331 }{ 729 } = (Scale Factor)^{3}\]

Answer 16

\[(Scale Factor)^{3} = 1.8258\]

Answer 17

\[Scale Factor = \sqrt[3]{1.8258}\]

Answer 18

1331.0082

Answer 19

ohh okay

Answer 20

so S.A of B = 0.00176 ?

Answer 21

605 = Scale factor ^2 x S.A of Smaller Solid

Answer 22

Sorry Cube root of 1.8258 is 1.22

Answer 23

Scale Factor is 1.22

Answer 24

\[\frac{ 605 }{ 1.22 \times 1.22 } = Surface Area of Smaller Solid\]

Answer 25

S.A of the smaller solid =404.46

Answer 26

yes

Answer 27

406.46

Answer 28

close

Answer 29

Answer Choice is C

Answer 30

thank you so much :)