To find the cost of silver to make one sphere, we first need to calculate the volume of the sphere and then determine the cost of the silver based on that volume.
The formula for the volume \( V \) of a sphere is given by:
\[ V = \frac{4}{3} \pi r^3 \]
where \( r \) is the radius of the sphere.
Given that the radius \( r \) is 1.5 cm and using \( \pi \approx 3.14 \), we can plug in the values:
\[ V = \frac{4}{3} \times 3.14 \times (1.5)^3 \]
First, calculate \( (1.5)^3 \):
\[ (1.5)^3 = 1.5 \times 1.5 \times 1.5 = 2.25 \times 1.5 = 3.375 \]
Now, substitute this back into the volume formula:
\[ V = \frac{4}{3} \times 3.14 \times 3.375 \]
Next, calculate \( \frac{4}{3} \times 3.14 \):
\[ \frac{4}{3} \times 3.14 \approx 4.18667 \text{ (repeating)} \]
Now multiply this by \( 3.375 \):
\[ V \approx 4.18667 \times 3.375 = 14.14225475 \]
So, the volume of the sphere is approximately \( 14.14225475 , \text{cm}^3 \).
Next, we need to find the cost of the silver required to make the sphere. Given that silver is priced at $6.00 per cm³, we calculate the cost as follows:
\[ \text{Cost} = \text{Volume} \times \text{Price per cm}^3 \]
Substituting in our values:
\[ \text{Cost} = 14.14225475 , \text{cm}^3 \times 6.00 , \text{dollars/cm}^3 \]
Calculating this gives:
\[ \text{Cost} = 84.8535285 \text{ dollars} \]
Thus, the silver cost to make one solid sphere is approximately $84.8535285.
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