Question

Two similar prisms have heights 4 cm and 10cm what is the ratio of their surface areas

2:5
4:25
8:125
16:625

Answer 1

Let k be the scale factor relating two similar prisms
`P_(1)` and
`P_(2)`, such that for corresponding parts of prisms
`P_(1)` and
`P_(2)` (for heights, in particular) we have
`k= (height\ of \ P_(1) )/(height \ of\ P_(2) )`. In our case
`k= (4)/(10) = (2)/(5)`.
For surfaces area we have
`(Surface \ area \ of \ P_(1) )/(Surface \ area \ of \ P_(2)) = k^(2) =( (2)/(5) )^(2)= (4)/(25)`.
So, the right answer is 4:25 (choice B)