A small hole in the wing of a space shuttle requires a 12.8cm^2 patch. What is the patch's area in square kilometers (km^2)? if the patching material costs NASA 3.21/in^2, what is the cost of the patch?
There are 100 cm in a m and 1000 m in a km; therefore,
12.8 cm x (1 m/100 cm)^2 x (1 km/1000 m)^2 = ?? or go to google and type in
12.8 square cm to square km and hit enter.
For the cost, I would convert cm^2 to in^2 first. There are 2.54 cm in 1 inch.
12.8 cm^2 x (1 inch/2.54 cm)^2 = ??, then find the cost. By the way, you don't have units for the cost per unit area. You may mean $3.21/in^2.
12.8cmx10^-9km^2
To find the patch's area in square kilometers, we need to convert the given area from square centimeters to square kilometers.
1 square kilometer (km^2) is equal to 1,000,000 square meters (m^2).
1 square meter (m^2) is equal to 10,000 square centimeters (cm^2).
Therefore, we can use the following conversions:
1 cm^2 = (1/10,000) m^2
1 m^2 = (1/1,000,000) km^2
Now, let's calculate the patch's area in square kilometers:
Area in m^2 = (12.8 cm^2) * (1/10,000 m^2/cm^2)
Area in m^2 = 0.00128 m^2
Area in km^2 = (0.00128 m^2) * (1/1,000,000 km^2/m^2)
Area in km^2 = 0.00000000128 km^2
Therefore, the patch's area in square kilometers is 0.00000000128 km^2.
To calculate the cost of the patch, we need to know the cost per square inch. The cost provided by NASA is $3.21/in^2.
To convert the area from square centimeters to square inches, we can use the conversion:
1 in^2 = 6.4516 cm^2
Now, let's calculate the cost of the patch:
Area in in^2 = (12.8 cm^2) * (1/6.4516 in^2/cm^2)
Area in in^2 = 1.984 in^2
Cost of the patch = (1.984 in^2) * ($3.21/in^2)
Cost of the patch = $6.37
Therefore, the cost of the patch is $6.37.
To find the patch's area in square kilometers (km^2), we need to convert the given area from square centimeters (cm^2) to square kilometers (km^2).
1 square kilometer (km^2) is equal to 1,000,000 square meters (m^2).
1 square meter (m^2) is equal to 10,000 square centimeters (cm^2).
So, to convert square centimeters (cm^2) to square kilometers (km^2), we use the following conversion factors:
1 km^2 = 1,000,000 m^2
1 m^2 = 10,000 cm^2
Given that the patch requires an area of 12.8 cm^2, we can convert it to square kilometers using these conversions:
12.8 cm^2 * (1 m^2 / 10,000 cm^2) * (1 km^2 / 1,000,000 m^2)
Calculating this, we find:
12.8 cm^2 * (1 / 10,000) * (1 / 1,000,000) km^2
= 0.00000128 km^2
Therefore, the patch's area is 0.00000128 square kilometers (km^2).
Now, let's calculate the cost of the patch using the given patching material cost of $3.21 per square inch (in^2).
The cost of the patch can be found by multiplying the cost per square inch by the area in square inches. To do this, we need to convert the patch area from square kilometers (km^2) to square inches (in^2).
1 square kilometer (km^2) is equal to 1,550,003.1 square inches (in^2).
So, to convert square kilometers (km^2) to square inches (in^2), we use the conversion factor:
1 km^2 = 1,550,003.1 in^2
Now, let's calculate the cost of the patch:
0.00000128 km^2 * 1,550,003.1 in^2 / 1 km^2 * $3.21 / 1 in^2
Simplifying this expression, we get:
0.00000128 * 1,550,003.1 * $3.21
Calculating this, we find:
Approximately $6.261 for the cost of the patch.