Question Video: Calculating the Volume and Density of an Object with Unit Conversion | Nagwa Question Video: Calculating the Volume and Density of an Object with Unit Conversion | Nagwa

Question Video: Calculating the Volume and Density of an Object with Unit Conversion Mathematics

A steel ball has a radius of 10 cm. If the density of the ball is 8,000 kg/m³, find the mass of the ball in kilograms. Give your answer to one decimal place.

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Video Transcript

A steel ball has a radius of 10 centimeters. If the density of the ball is 8,000 kilograms per cubic meter, find the mass of the ball in kilograms. Give your answer to one decimal place.

We are told that we have a ball with radius 10 centimeters. The volume of any ball or sphere is equal to four-thirds 𝜋𝑟 cubed. This means that we could calculate the volume of the ball in cubic centimeters by substituting 𝑟 equals 10 into the formula. As our units for density were kilograms per cubic meter, we actually need to convert the radius into meters first. As there are 100 centimeters in one meter, 10 centimeters will be equal to 0.1 meters.

We can therefore calculate the volume of the ball in cubic meters by multiplying four-thirds by 𝜋 by 0.1 cubed. Typing this into the calculator gives us an answer of 0.004188 and so on. We were asked to calculate the mass of the ball, which means this isn’t the final answer. We will therefore not round at this stage.

We know that the density of any object is equal to its mass divided by its volume. We can rearrange this formula so that the mass is equal to the density multiplied by the volume. The mass of the ball will be equal to 8,000 multiplied by 0.004188 and so on. This is equal to 33.5103 and so on. Rounding to one decimal place, we get an answer of 33.5. A steel ball with a radius of 10 centimeters, or 0.1 meters, and a density of 8,000 kilograms per cubic meter has a mass of 33.5 kilograms.

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