Hi, can you please help me solve the following problem? It\'s notfrom a textbook

Question

Hi, can you please help me solve the following problem? It's notfrom a textbook, but we use the Giancoli Textbook as a resource.Thank you!

Problem 4. An asteroid of a highly irregular shapemeasures 10.1 m across its longest length. At your disposal, youhave an exact scale replica of the asteroid, and your goal is todetermine the volume of the actual asteroid. You measure two thingsabout the replica:

First, that it measures 5.23 cm across its longestlength; and second, that the volume of the replica is 138cm3 (you might have done the volume measurement bysubmerging the replica into water in a graduated cylinder, and thenobserving by how much the water level rose as a result). Based onthis information, you can compute the volume of the actualasteroid. What is it, in m3? (Hint: what if the asteroidand the replica were perfect cubes? Perfect spheres?)

Explanation / Answer

Sice replica is proportional to the actual asteroid in alldimensions we can state a/A = 0.0523 / 10.1 is a constant and this gives us a scaleS S= a/A = 0.0523 / 10.1= 0.0051 or 1: 193 Voluem V is a product of width w length l and height h V= w l h then asteroids actual voluem is V= v (1/S)3 ( we have to considerscaling in all three dimensions hance we have to cube (1/S)) V=138 (193)3 = 9.92x108cm3 V= 992 m3 Please let me know if you have any questions. Please let me know if you have any questions.

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