A troy ounce is a unit of mass used for precious metals such as gold. There are 12 troy ounces in a troy pound and a troy pound is equivalent to 373.3 grams. If the density of gold is 19.3 grams per cubic centimeter, which of the following is closest to the number of cubic centimeters in the volume of block of gold with mass of 5 troy ounces? [ Note: density is mass divided by volume]

Options

A. `7`
B. `8`
C. `9`
D. `10`

Answer

To solve the problem of finding the volume of a block of gold with a mass of 5 troy ounces, we will follow these steps:

### Step 1: Convert troy ounces to grams
We know that:
- 1 troy pound = 373.3 grams
- 1 troy pound = 12 troy ounces

First, we need to find out how many grams are in 5 troy ounces.

Using the conversion:
\[ 1 \text{ troy ounce} = \frac{373.3 \text{ grams}}{12 \text{ troy ounces}} \approx 31.1083 \text{ grams} \]

Now, we can calculate the mass of 5 troy ounces:
\[ \text{Mass of gold} = 5 \text{ troy ounces} \times 31.1083 \text{ grams/troy ounce} \approx 155.54 \text{ grams} \]

### Step 2: Use the density to find the volume
We know that:
\[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \]

Given that the density of gold is 19.3 grams per cubic centimeter, we can rearrange the formula to find the volume:
\[ \text{Volume} = \frac{\text{Mass}}{\text{Density}} \]

Substituting the values we have:
\[ \text{Volume} = \frac{155.54 \text{ grams}}{19.3 \text{ grams/cm}^3} \approx 8.06 \text{ cm}^3 \]

### Step 3: Round the volume to the nearest whole number
The volume of the block of gold is approximately 8.06 cm³. Rounding this to the nearest whole number gives us:
\[ \text{Volume} \approx 8 \text{ cm}^3 \]

### Final Answer
The volume of the block of gold with a mass of 5 troy ounces is approximately **8 cm³**.

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