Question

What's the surface area ratio & the volume ratio??

please help me ASAP!!

Answer 1

Explanation:

Volumes of two spheres A and B = 648 cm³ and 1029 cm³

Things to remember:

1). Scale factor of two objects =
`(r_1)/(r_2)` [
`r_1` and
`r_2` are the radii of two circles]

2). Area scale factor =
`((r_1)^2)/((r_2)^2)`

3). Volume scale factor =
`((r_1)^3)/((r_2)^3)`

Volume scale factor Or Volume ratio =
`(V_A)/(V_B)`

`((r_1)^3)/((r_2)^3)= (648)/(1029)`

`(r_1)/(r_2)=\sqrt[3]{(648)/(1029) }`

`(r_1)/(r_2)=\frac{6(\sqrt[3]{3})}{7(\sqrt[3]{3})}`

`(r_1)/(r_2)=(6)/(7)`

Therefore, scale factor =
`(r_1)/(r_2)=(6)/(7)`

≈ 6 : 7

Area scale factor Or area ratio =
`((r_1)/(r_2))^2=((6)/(7))^2`

=
`(36)/(49)`

≈ 36 : 49

Volume scale factor or Volume ratio =
`(648)/(1029)`

=
`(216)/(343)`

≈ 216 : 343