Edith wants to make a paperweight at pottery class. She wants the paperweight to have a pyramid-like shape with a base area of \[120\] square centimeters, and she wants it to weigh \[400\] grams. The density of the clay she is using is \[1.6\] grams per cubic centimeter. What should be the height of the paperweight?
Question
Edith wants to make a paperweight at pottery class. She wants the paperweight to have a pyramid-like shape with a base area of square centimeters, and she wants it to weigh grams. The density of the clay she is using is grams per cubic centimeter. What should be the height of the paperweight?
Solution
To find the height of the paperweight, we first need to find the volume of the clay that Edith will use. We know that the weight of the clay is 400 grams and the density is 1.6 grams per cubic centimeter.
The formula to find the volume when you know the mass and the density is:
Volume = Mass / Density
So, we substitute the given values into the formula:
Volume = 400 grams / 1.6 grams per cubic centimeter = 250 cubic centimeters
Now, we know that the paperweight is in the shape of a pyramid. The formula for the volume of a pyramid is:
Volume = 1/3 * Base Area * Height
We know the volume and the base area, so we can rearrange the formula to solve for the height:
Height = Volume / (1/3 * Base Area)
Substitute the given values into the formula:
Height = 250 cubic centimeters / (1/3 * 120 square centimeters) = 250 / 40 = 6.25 centimeters
So, the height of the paperweight should be 6.25 centimeters.
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