Question

What is the total surface area ratio of following similar solids?30 mi45 mi60 mi90 mi09:4O 15:6O 5:4O 3:2

Answer 1

Solid A has five(5) rectangular blocks that are co-joined. The dimension of each, is 45miles by 90miles.

Thus,

`\begin{gathered} Total\text{ surface area=5}* Area\text{ of one rectangular block} \\ \text{Total Surface Area=5}*(45*90) \\ T\mathrm{}S\mathrm{}A=5*4050 \\ T\mathrm{}S\mathrm{}A=20250mi^2 \end{gathered}`

Solid B has five(5) rectangular blocks that are co-joined. The dimension of each, is 30mi by 60mi.

Thus,

`\begin{gathered} \text{Total Surface Area= 5}* Area\text{ of one rectangular block} \\ T\mathrm{}S\mathrm{}A=5*(30*60) \\ T\mathrm{}S\mathrm{}A=5*1800 \\ T\mathrm{}S\mathrm{}A=9000mi^2 \end{gathered}`

The ratio of the T.S.A of the similar solids is given below:

`\begin{gathered} T\mathrm{}S\mathrm{}A_{solid\text{ A}}\colon T.S.A_{solid\text{ B}} \\ 20250\colon9000 \\ \text{Divide both by 2250, we have:} \\ 9\colon4 \end{gathered}`

Hence, the correct option is Option A