Question
A hollow ball is made of rubber that is 2 centimeters thick. The ball has a radius to the outside surface of 6 centimeters.
What is the approximate volume of rubber used to make the ball?
Use 3.14 for pi
33.5 cm^3
267.9 cm ^3
636.4 cm ^3
904.3 cm ^3
What is the approximate volume of rubber used to make the ball?
Use 3.14 for pi
33.5 cm^3
267.9 cm ^3
636.4 cm ^3
904.3 cm ^3
Answers
GPT-4o mini
To find the volume of rubber used in making the hollow ball, we will calculate the volume of the outer sphere (the ball) and subtract the volume of the inner sphere (the hollow part).
1. **Find the outer radius**: The outer radius is given as 6 cm.
2. **Calculate the inner radius**: Since the rubber is 2 cm thick, the inner radius will be:
\[
\text{Inner radius} = \text{Outer radius} - \text{Thickness} = 6 \text{ cm} - 2 \text{ cm} = 4 \text{ cm}
\]
3. **Volume of the outer sphere**: The formula for the volume \(V\) of a sphere is given by:
\[
V = \frac{4}{3} \pi r^3
\]
For the outer sphere (radius = 6 cm):
\[
V_{\text{outer}} = \frac{4}{3} \times 3.14 \times (6)^3
\]
First, calculate \(6^3\):
\[
6^3 = 216
\]
Now substitute:
\[
V_{\text{outer}} = \frac{4}{3} \times 3.14 \times 216 \approx 904.32 \text{ cm}^3
\]
4. **Volume of the inner sphere**: For the inner sphere (radius = 4 cm):
\[
V_{\text{inner}} = \frac{4}{3} \times 3.14 \times (4)^3
\]
First, calculate \(4^3\):
\[
4^3 = 64
\]
Now substitute:
\[
V_{\text{inner}} = \frac{4}{3} \times 3.14 \times 64 \approx 267.93 \text{ cm}^3
\]
5. **Volume of rubber used**: Now subtract the volume of the inner sphere from the volume of the outer sphere:
\[
V_{\text{rubber}} = V_{\text{outer}} - V_{\text{inner}} \approx 904.32 \text{ cm}^3 - 267.93 \text{ cm}^3
\]
\[
V_{\text{rubber}} \approx 636.39 \text{ cm}^3
\]
The approximate volume of rubber used to make the ball is therefore \( \approx 636.4 \text{ cm}^3 \).
So, the correct option is:
**636.4 cm³**.
1. **Find the outer radius**: The outer radius is given as 6 cm.
2. **Calculate the inner radius**: Since the rubber is 2 cm thick, the inner radius will be:
\[
\text{Inner radius} = \text{Outer radius} - \text{Thickness} = 6 \text{ cm} - 2 \text{ cm} = 4 \text{ cm}
\]
3. **Volume of the outer sphere**: The formula for the volume \(V\) of a sphere is given by:
\[
V = \frac{4}{3} \pi r^3
\]
For the outer sphere (radius = 6 cm):
\[
V_{\text{outer}} = \frac{4}{3} \times 3.14 \times (6)^3
\]
First, calculate \(6^3\):
\[
6^3 = 216
\]
Now substitute:
\[
V_{\text{outer}} = \frac{4}{3} \times 3.14 \times 216 \approx 904.32 \text{ cm}^3
\]
4. **Volume of the inner sphere**: For the inner sphere (radius = 4 cm):
\[
V_{\text{inner}} = \frac{4}{3} \times 3.14 \times (4)^3
\]
First, calculate \(4^3\):
\[
4^3 = 64
\]
Now substitute:
\[
V_{\text{inner}} = \frac{4}{3} \times 3.14 \times 64 \approx 267.93 \text{ cm}^3
\]
5. **Volume of rubber used**: Now subtract the volume of the inner sphere from the volume of the outer sphere:
\[
V_{\text{rubber}} = V_{\text{outer}} - V_{\text{inner}} \approx 904.32 \text{ cm}^3 - 267.93 \text{ cm}^3
\]
\[
V_{\text{rubber}} \approx 636.39 \text{ cm}^3
\]
The approximate volume of rubber used to make the ball is therefore \( \approx 636.4 \text{ cm}^3 \).
So, the correct option is:
**636.4 cm³**.