Question

Determine whether each statement is sometimes, always, or never true. If the scale factor of two similar solids is a:b, then the ratio of their surface areas is a:b. Question 4 options:

always



never



sometimes

Answer 1

never is correct.

Explanation:

Answer 2

never

Explanation:

let k be the scale ratio of two bodies then according to the question

k = a/b -- (1)

let Sa be the surface area of body A and Sb be the surface area of body B , then

according to the relation of scale factor and surface areas

`k^(2)  Sa = Sb`

from the above equation ,

`Sa/Sb = 1/k^(2)`

as k = a/b from (1)

therefore
`Sa/Sb=1/(a/b)^(2) \\Sa/Sb = b^(2) /a^(2)`

hence the ratio of their surface area is
`b^(2) /a^(2)`