Question

1. the density of gold is 18 g/cm³. if the volume of a piece of gold is 13 cm³, how many grams will it be? 2. a shipping company is sending a fragile package with these dimensions: 6 in. x 7 in. x 2 in. if the box they use to send it is 9 in. x 9 in. x 3 in., how many cubic inches of packing peanuts can they fit into the box?

Explanation:

For the shipping company problem:

Step1: Recall volume formula for a rectangular box

The volume \( V \) of a rectangular box is given by \( V = l \times w \times h \), where \( l \) is length, \( w \) is width, and \( h \) is height.

Step2: Identify the dimensions

Here, \( l = 6 \) in, \( w = 7 \) in, \( h = 2 \) in.

Step3: Calculate the volume

Substitute the values into the formula: \( V = 6 \times 7 \times 2 \). First, \( 6\times7 = 42 \), then \( 42\times2 = 84 \).

Step1: Recall density formula

Density \(
ho \) is given by \(
ho=\frac{m}{V} \), where \( m \) is mass and \( V \) is volume. We need to find \( m \), so rearrange the formula to \( m =
ho\times V \).

Step2: Identify the values

Given \(
ho = 18 \) g/cm³ and \( V = 13 \) cm³.

Step3: Calculate the mass

Substitute the values: \( m = 18\times13 \). \( 18\times13 = 234 \).

Answer:

84 cubic inches

For the gold density problem: