How big is a ton? That is, what is the volume of something that weighs a ton? To be specific, estimate the diameter of a 1-ton rock, but first make a wild guess: will it be 1ft across, 3ft, or the size of a car? [Hint: Rock has mass per volume about 3 times that of water, which is 1kg per Liter (1000cm^3) or 62lbs per cubic foot.]
I have this question from a worksheet and don't know quite what it's asking....
So far I've gotten that the volume is 333.3 (repeating) Liters, but I don't understand how to determine the dimensions based on that.
Divide the mass (1000 kg) by the density to get the volume of a rock. Assume the density is three times that of water. You can assume the rock is a sphere or cube to get the approximate dimension from the volume.
The density of water is 1000 kg/m^3
The question is asking you to estimate the diameter of a rock that weighs one ton. To make this estimation, we can use the hint provided in the question, which tells us that the mass per volume of a rock is about 3 times that of water.
First, let's convert the given mass per volume of water from pounds per cubic foot to kilograms per liter. We have:
1 pound = 0.453592 kg
1 cubic foot = 28.3168 liters
So, the mass per volume of water is approximately:
(62 lbs/ft^3) * (0.453592 kg/lb) / (28.3168 L/ft^3) ≈ 1.000 g/cm^3
Now, we know that a rock has a mass per volume about 3 times that of water, so it would be approximately:
3 g/cm^3
To estimate the diameter of the rock, we need to calculate its volume first. Since we know the mass and the mass per volume of the rock, we can find the volume using the formula:
Volume = Mass / Mass per volume
For a one-ton rock, which has a mass of approximately 1000 kg, the volume would be:
1000 kg / 3 g/cm^3 ≈ 333.33 cm^3
Now, the volume of a sphere is given by the formula:
Volume = (4/3) * π * r^3
Since we are looking for the diameter of the rock, we need to calculate the radius. Rearranging the formula, we get:
r = (3 * Volume / (4 * π))^(1/3)
Inserting the volume we calculated, we have:
r = (3 * 333.33 cm^3 / (4 * π))^(1/3)
Calculating this value, we get:
r ≈ 4.404 cm
Finally, to find the diameter, we double the radius:
Diameter ≈ 2 * 4.404 cm ≈ 8.808 cm
Therefore, the estimated diameter of a 1-ton rock would be approximately 8.808 cm.
The question is asking about the size or volume of something that weighs a ton. In this case, you need to estimate the diameter of a 1-ton rock. To do that, we first need to understand what a ton represents.
A ton is a unit of weight commonly used to measure heavy objects. There are two main types of tons: the short ton and the metric ton. In this case, we will be considering the short ton, also known as the US ton, which is equal to 2,000 pounds or approximately 907 kilograms.
The hint in the question mentions that the mass per volume of rock is about three times that of water. Water has a mass of 1 kilogram per liter (or 1,000 cubic centimeters) or 62 pounds per cubic foot. This gives us an idea of the rock's density relative to water.
Now, in order to estimate the diameter of a 1-ton rock, we need to make an educated guess based on its volume. To calculate the volume, we need the density of the rock. Assuming the rock has a density similar to three times that of water, we can say that it would have a density of approximately 186 pounds per cubic foot.
To find the volume of a 1-ton rock, we can divide its weight by its density. Since 1 ton is equal to 2,000 pounds, we can calculate:
Volume = Mass / Density = 2,000 pounds / 186 pounds per cubic foot ≈ 10.75 cubic feet
Now, to estimate the diameter of the rock, let's assume it has a spherical shape. The volume of a sphere is given by the formula:
Volume = (4/3) π r^3
By rearranging the formula, we can solve for the radius (r):
r = (3V / (4π))^(1/3)
Substituting the volume we found earlier:
r = (3 * 10.75 ft^3 / (4π))^(1/3) ≈ 1.05 feet
Multiplying the radius by 2, we can estimate the diameter:
Diameter ≈ 1.05 feet * 2 = 2.1 feet
Therefore, the estimated diameter of a 1-ton rock would be approximately 2.1 feet.