Question

Suppose you need to place 81.0 pounds of a solid material with density 20.00 g/mL onto a satellite, so that it will orbit the Earth. How many cubic inches of space would you need on the satellite for this material? Use these conversion factors: 2.2 lbs = 1 kg, 2.54 cm = 1 inch. Also use the usual metric conversion factors, such as kg to g. Your answer should be in three significant figures, even if Canvas might use more or less.

Answer 1

Following is the - complete Answer -&- Explanation, for the given Question, in......typed format...

Answer:

The solid material, will occupy volume = 112.1 inch³( i.e. cubic inches ) , i.e. correct up to 3 significant figures.  

Explanation:

Following is the complete Explanation, for the above Answer...

• Given:

1. Mass of the solid material = 81.0 lb ( pounds )
2. Density of the solid material:   =  20.0 g/mL ( grams per milli-liters )

• ​​​​​​​Step - 1:

​​​​​​​ We know: 1.0 lb = 0.453592 kg ( kilo-grams ) =  0.4536 kg ( approx. )

Therefore:

Mass of the solid material =  ( 81.0 lb ) x ( 0.4536 kg / lb ) = 36.7416 kg =  36741.6 g ( grams )

Volume of the solid material =  ( 36741.6 g ) / ( 20.0 g/mL ) = 1837.08 mL OR 1837.08 cm³   

• Step - 2:

​​​​​​​We are given with the following information:

2.54 cm = 1.0 inch

Therefore:

1.0 cm = 0.3937 inch

1.0 cm³ = 0.061 inch³   

• Step - 3:

​​​​​​​Using the above information, we can convert the volume, of the solid material, from cm³to  inch³  as the following:

Therefore:

Volume of the solid material =  1837.08 cm³ = ( 1837.08 cm³ ) x ( 0.061 inch³ / cm³ ) =  112.105 inch³

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