Two similar solids whose densities are each 1g/cm^3. are such that the first has a height of 5cm and a volume of 120cm^3.the second has a mass of 3240g.find the height of the second solid
Convert g to cm then find volume scale factor then linear scale factor then equate and get the answer
Let's begin by finding the volume scale factor.
The first solid has a volume of 120 cm^3 and a height of 5 cm.
Volume of the first solid = height * base area
120 cm^3 = 5 cm * base area
Therefore, the base area of the first solid is 120 cm^3 / 5 cm = 24 cm^2.
Now, let's find the base area of the second solid.
The second solid has a volume of 3240 cm^3.
Volume of the second solid = height * base area
3240 cm^3 = height * base area
We already know that the base area of the first solid is 24 cm^2.
Therefore, the base area of the second solid is 3240 cm^3 / height.
Now, let's find the height of the second solid.
3240 cm^3 / height = 24 cm^2
To eliminate cm^2, divide both sides by 24 cm^2:
3240 cm^3 / height = 24 cm^2
3240 cm^3 / 24 cm^2 = height
Simplifying, we get:
135 cm = height
Therefore, the height of the second solid is 135 cm.
To find the height of the second solid, we need to use the information given about the first solid, its volume, and the fact that both solids have the same density.
First, let's find the mass of the first solid, using the formula:
Mass = Density * Volume
Since the density of both solids is 1g/cm³ and the volume of the first solid is 120cm³, we can substitute these values into the formula:
Mass = 1g/cm³ * 120cm³ = 120g
Now, since both solids have the same density, the second solid also has a density of 1g/cm³. We know the mass of the second solid, which is given as 3240g. To find the volume of the second solid, we can rearrange the formula:
Volume = Mass / Density
Substituting the given values into the formula, we get:
Volume = 3240g / 1g/cm³ = 3240cm³
Finally, to find the height of the second solid, we need to divide its volume by its base area. Since the base area of both solids is the same, dividing the volume by the base area will give us the height of the solid.
To find the base area, we need to use the formula:
Base Area = Volume / Height
Rearranging the formula, we get:
Height = Volume / Base Area
In this case, we don't have the dimensions of the base, so we cannot calculate the height of the second solid without that information.
The larger has a volume of 3240 cm^3(why?)
since volume grows as the cube of the scale factor,
(h/5)^3 = 3240/120
Now solve for h.