Question

alexis wants to make a paperweight at pottery class. he designs a pyramid - like model with a base area of 100 square 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? \boxed{} grams per cubic centimeter show calculator

Explanation:

Step1: Calculate the volume of the pyramid

The formula for the volume \( V \) of a pyramid is \( V=\frac{1}{3}Bh \), where \( B \) is the base area and \( h \) is the height. Given \( B = 100\space cm^{2} \) and \( h=6\space cm \), we substitute these values into the formula:
\( V=\frac{1}{3}\times100\times6 \)
\( V = 200\space cubic\space centimeters \)

Step2: Calculate the density

Density \(
ho \) is given by the formula \(
ho=\frac{m}{V} \), where \( m \) is the mass and \( V \) is the volume. We know the mass \( m = 300\space grams \) (since we want the lowest density for the minimum weight of 300 grams) and the volume \( V = 200\space cubic\space centimeters \) from Step 1. Substituting these values:
\(
ho=\frac{300}{200} \)
\(
ho = 1.5\space grams\space per\space cubic\space centimeter \)

Answer:

\( 1.5 \)