Question

11.9 cm
.
.
.
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Part 1
An oil candle globe made of​ hand-blown glass has a diameter of 23.8 cm. What is the volume of the​ globe?
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Part 1
Volumeequals
  
enter your response here cm cubed
​(Use 3.14 for pi. Round to the nearest​ hundredth.)

Answer 1

To find the volume of a sphere, you can use the formula:

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

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

1. First, we need to find the radius of the globe. The diameter is given as 23.8 cm, so the radius \( r \) is half of that:

\[
r = \frac{23.8 \, \text{cm}}{2} = 11.9 \, \text{cm}
\]

2. Now, substitute \( r \) into the volume formula:

\[
V = \frac{4}{3} \pi (11.9)^3
\]

3. Calculate \( (11.9)^3 \):

\[
(11.9)^3 \approx 1685.859
\]

4. Substitute \( (11.9)^3 \) into the volume formula:

\[
V \approx \frac{4}{3} \times 3.14 \times 1685.859
\]

5. Calculate the volume:

\[
V \approx \frac{4}{3} \times 3.14 \times 1685.859 \approx \frac{4 \times 3.14 \times 1685.859}{3} \approx \frac{21171.5873}{3} \approx 7057.1958
\]

6. Finally, round to the nearest hundredth:

\[
V \approx 7057.20 \, \text{cm}^3
\]

So the volume of the globe is approximately \( 7057.20 \, \text{cm}^3 \).