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Chapter 1: Problem 46

One cubic centimeter of water has a mass of 1 gram. A milliliter is equal to a cubic centimeter. What is the mass, in kilograms, of a liter of water? A metric ton is a thousand kilograms. How many cubic centimeters of water are in a metric ton of water? If a metric ton of water were held in a thin-walled cubical tank, how long (in meters) would each side of the tank be?

Short Answer

Expert verified
Answer: The length of each side of a cubical tank that holds a metric ton of water is 1 meter.

Step by step solution

01

Convert mass of a liter of water to kilograms

First, we need to find the mass of a liter of water in kilograms. Since there are 1000 milliliters (mL) in a liter and every milliliter is equal to a cubic centimeter, we must multiply the number of milliliters in a liter by the mass of a cubic centimeter of water (1 gram) and convert grams to kilograms. 1 liter = 1000 mL = 1000 cubic centimeters Mass of 1 liter of water = (1000 cubic centimeters x 1 gram per cubic centimeter) x (1 kilogram per 1000 grams)
02

Calculate volume of a metric ton of water in cubic centimeters

Now, we want to find out the volume of a metric ton of water, which is equal to 1000 kilograms. To do this, we will divide the mass of water by the mass of 1 cubic centimeter of water. Volume of a metric ton of water = (1000 kg / 1 kg) × 1000 cubic centimeters Volume of a metric ton of water = 1000 × 1000 cubic centimeters
03

Find the length of each side of a cubical tank in meters

A cube has equal sides, so the volume of a cube is given by the equation: Volume = side^3. We will use this equation to calculate the length of each side of the cubical tank that holds a metric ton of water. To change cubic centimeters to cubic meters, divide by 1,000,000 (since there are 1,000,000 cubic centimeters in a cubic meter). 1 metric ton of water = 1000000 cubic centimeters = 1 cubic meter Side^3 = 1 m^3 To find the length of each side, take the cube root of the volume: Side = (1 m^3)^(1/3) Side = 1 meter So, each side of the tank would measure 1 meter in length.

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