A nickel pyramidal paper weight has a square base of sides 5 cm and a height of 3 cm. What is the mass of a dozen such paper weights if the mass of 1 cm^3 of nickel is 8.9g?
volume of pyramid = (1/3)base x height
= (1/3)(25)(3)
= 25 cm^3
so one pyramid has a mass of 25(8,9) g
then a dozen would have a mass of
25(12)(8.9) g
or 2670 g
the question's answer given above is osmly designed
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To find the mass of a dozen nickel pyramidal paper weights, we need to calculate the volume of one paperweight, then multiply it by 12 and finally multiply it by the mass of 1 cm^3 of nickel.
1. Calculate the volume of one nickel pyramidal paperweight:
The volume of a pyramid is given by the formula: V = (1/3) * base area * height.
In this case, the base is a square with sides of 5 cm, so the base area is 5 cm * 5 cm = 25 cm^2.
The height of the pyramid is 3 cm.
Therefore, the volume of one paperweight is: V = (1/3) * 25 cm^2 * 3 cm = 25 cm^3.
2. Calculate the mass of one paperweight:
Since the density of nickel is given as 8.9 g/cm^3, we can multiply the volume by the density to get the mass.
Mass = Volume * Density = 25 cm^3 * 8.9 g/cm^3 = 222.5 g.
3. Calculate the mass of a dozen paperweights:
Multiply the mass of one paperweight by 12:
Mass of a dozen paperweights = 222.5 g * 12 = 2670 g.
Therefore, the mass of a dozen nickel pyramidal paperweights is 2670 grams.
To find the mass of a dozen nickel pyramidal paper weights, we first need to calculate the volume of one paper weight and then multiply it by twelve.
The volume of a pyramid can be found using the formula:
Volume = (1/3) * Base Area * Height
The base of the pyramid is square, so the base area is equal to the square of the length of one side. In this case, the base has sides of 5 cm, so the base area is 5 cm * 5 cm.
Now we can calculate the volume of one paper weight:
Volume = (1/3) * (5 cm * 5 cm) * 3 cm
Volume = (1/3) * 25 cm^2 * 3 cm
Volume = 25 cm^2 * cm * cm/3 cm
Volume = 25 cm^3
Next, we need to find the mass of one paper weight. Since we know that the mass of 1 cm^3 of nickel is 8.9g, we can multiply the volume of one paper weight by the mass of 1 cm^3 of nickel:
Mass of one paper weight = 25 cm^3 * 8.9g/cm^3
Mass of one paper weight = 222.5g
Finally, to find the mass of a dozen paper weights, we multiply the mass of one paper weight by twelve:
Mass of a dozen paper weights = 222.5g * 12
Mass of a dozen paper weights = 2670g
Therefore, the mass of a dozen nickel pyramidal paper weights is 2670 grams.