Question

A small hole in the wing of a space shuttle requires a 20.7-cm² patch. (a) What is the patch’s area in square kilometers (km² )? (b) If the patching material costs NASA $3.25/in2 , what is the cost of the patch?

Answer 1

Solution

$\text{a)}$

Area of the hole in $\text{cm}$ ${}^2$ is $\text{20,7cm}$ ${}^2$ . We have to convert it to $\text{km}$ ${}^2$.

$\text{1cm}$ =10${}^{-5}$ $\text{km}$

$\text{1cm}$ ${}^2$=(10${}^{-5}$)${}^2$ $\text{km}$ ${}^2$

$\text{1cm}$ ${}^2$=10${}^{-10}$ $\text{km}$ ${}^2$

So $\text{20,7cm}$ ${}^2$=20,7*10${}^{-10}$ $\text{km}$ ${}^2$

$\text{20,7cm}$ ${}^2$=2,07*10${}^{-9}$ $\text{km}$ ${}^2$

 

$\text{b)}$

We have to calculate the cost of repair. For that we first have to convert area to in${}^2$.

1 $\text{cm}$=0.3937 $\text{in}$

1 $\text{cm}$ ${}^2$=(0.3937)${}^2$ $\text{in}$ ${}^2$

1 $\text{cm}$ ${}^2$=0,155 $\text{in}$ ${}^2$

so 20,7$\text{cm}$ ${}^2$=20,7*0,155 $\text{in}$ ${}^2$

20,7$\text{cm}$ ${}^2$=3,2085 $\text{in}$ ${}^2$

and the cost is 3,25 dollars per $\text{in}$ ${}^2$

 

so total cost = 3,2085* 3,25 dollars= $\text{10,427625 dollars}$

Therefore,

$\text{a)}$ $\text{20,7cm}$ ${}^2$=2,07*10${}^{-9}$ $\text{km}$ ${}^2$

$\text{b)}$ Total cost if the patch is $\text{10,428 dollars}$