Question

Alexis wants to make a paperweight at pottery class. He designs a pyramid-like model with a base area of 100square centimeters and a height of 6 centimeters. He wants the paperweight to weigh at least 300 grams. What is the lowest possible density of the material Alexis uses to make the paperweight?

Answer 1

The lowest possible density of the material Alexis uses to make the paperweight is 1.5 g/cm³

Explanation:

Here we have the volume of a pyramid given by the following relation;

`Volume \ of \ pyramid = (1)/(3) * Base \ Area * Height`

Therefore the volume, V of the pyramid is equal to 1/3 × 100 cm × 6 cm = 200 cm³

The density of the paperweight is given by
`Density = (Mass)/(Volume)`

The required density is then
`Required \ Density = (300 \, g)/(200 \, cm^3) = 1.5 \, g/cm^3`

The lowest possible density of the material Alexis uses to make the paperweight is therefore 1.5 g/cm³.

Answer 2

The density of the material must be at least 1.5 g/cm³.

Explanation:

The volume for a pyramid is given by the following formula:

V = (1/3)*Abase*h

Where V is the volume, Abase is the base area and h is the height. For Alexis's pyramid, we have:

V = (1/3)*100*6 = 200 cm³

Since he wants the paperweigth to have a mass of at least 300 grams, the density must be at least:

density = mass/volume = 300/200 = 1.5 g/cm³