Question

The surface areas of two similar hexagonal prisms are 882cm² and 1,058 cm²? What is the scale factor of the smaller

prism to the larger prism?
A. 882/1,058
B. 21/23
C. 23/21
D. 21/11​

Answer 1

scale factor of the smaller prism to the larger prism is B. 21/23

Explanation:

Given

surface areas of two similar hexagonal prisms are 882cm² and 1,058 cm²?

scale factor is ratio of sides of two similar objects

thus scale factor for given prism will be = side of smaller prism / side of larger prism

in general rule

If shape of solid has scale factor of k

scale factor of area = k²

scale factor of volume = k³

_____________________________

Given in the problem area of two prism is given

we know area = side^2

scale factor of area = k²

k^2 = area of smaller prism / area of larger prism

`k^2 = 882 / 1058 = 441/529\\k = √( 441/529) \\k = 21/23`

Thus, correct option is B 21/23.