Math Help: Density and Volume Relation?

For the first expression (not equation), you would have to move the "−4" part too. 8+2−4 could also be written as 8+2+(-4). Since you're adding by -4, you have to include the negative as well.

For the second questions, using the density, you have to find the mass of the snowball.

First, find the volume of the snowball. Since the diameter is 10 cm, the radius is 5 cm.

V = (4/3)πr³ = (4/3)π(5)³ = (500/3)π cm³

The formula for density is D = M/V. Just plug in the values and solve for M (the mass).

D = M/V

0.75 g/cm³ = M/(500/43)π cm³

M = (500/3)π cm³ × 0.75 g/cm³ = 125π grams

This is how much the snowball weighs, about 392.7 grams.

Even though the snow melts, the mass of water will be the same as the mass of the snow, assuming now evaporation or loss of water takes place. Now we can plug into the density formula once more, and solve for the volume of water.

D = M/V

1.0 g/cm³ = (125π g)/V

V = (125π g)/(1.0 g/cm³) = 125π cm³ ≈ 392.7 cm³.

The volume of a cylinder is given by the following formula:

V = πr²h, where h is the height (or depth, in this case)

Since the water will just fill the cylinder up, we can make h the depth of the water (since the height of the cylinder is irrelevant).

V = πr²h

125π cm³ = π(6)²h

125π cm³ = 36πh

h = 3.47222... cm

That is not an equation; it doesn't have an equals sign. It's an expression. If you're moving it around in an expression, then you move the 4 with its sign. However, no matter which order you add or subtract them, you should always come out with the same answer.

And I'm pretty sure I already answered your second question. The volume of the snowball and the volume of the water are different. You're not going to have the same volume once it melts. Therefore, you need the density to find the mass of the matter because according to the law of conservation of mass/matter, the mass will stay the same between the two different forms. You can't just find the volume of the snowball and stick it into the can and keep its volume the same when it melts and find the height that way. Density is mass/volume.

Volume of sphere = (4/3)πr^3, where r is the radius

Volume of cylinder = πr^2h, where r is the radius and h is the height

The snowball has a diameter of 10 cm, so its radius is 5 cm, which makes its volume V = (4/3)π(5)^3 = about 523.599 cubic centimeters. Its density is 0.75 g/cm^3, so the mass of the snow is (523.599 cm^3)(0.75 g/cm^3) = 392.699 grams.

According to the law of conservation of mass/matter, when the snowball melts into water, it will still have the same mass even though it will not have the same volume. The density of water is 1 g/cm^3, so the volume of the water is (392.699 g)/(1 g/cm^3) = 392.699 cm^3. The cylindrical can has a diameter of 12 cm, which is a radius of 6 cm, so its volume that we know is π(6)^2h = 36πh. Now set this equal to the volume of the water to solve for its height.

36πh = 392.699

h = about 3.47 cm <===ANSWER