An oil candle globe made of​ hand-blown glass has a diameter of 25.6 cm. What is the volume of the​ globe?

1 answer

To calculate the volume of a globe (which is a sphere), we can use the formula for the volume of a sphere:

\[ V = \frac{4}{3} \pi r^3 \]

where \( V \) is the volume and \( r \) is the radius of the sphere.

First, we need to find the radius. The radius is half of the diameter:

\[ r = \frac{d}{2} = \frac{25.6 , \text{cm}}{2} = 12.8 , \text{cm} \]

Now we can substitute the radius into the volume formula:

\[ V = \frac{4}{3} \pi (12.8 , \text{cm})^3 \]

Calculating \( (12.8)^3 \):

\[ 12.8^3 = 209.152 , \text{cm}^3 \]

Now we substitute this value back into the volume formula:

\[ V = \frac{4}{3} \pi (209.152) \approx \frac{4}{3} \times 3.14159 \times 209.152 \]

Calculating the volume:

\[ V \approx \frac{4}{3} \times 3.14159 \times 209.152 \approx \frac{4 \times 3.14159 \times 209.152}{3} \]

\[ V \approx \frac{2637.6964}{3} \approx 879.2321 , \text{cm}^3 \]

Thus, the volume of the oil candle globe is approximately:

\[ \boxed{879.23 , \text{cm}^3} \]