Question
Consider a cube with a volume of 64 cm3
. What can be concluded about the cube? Select the two that apply.(2 points)
Responses
The expression s2
, where s represents the side length was used to solve this problem.
The expression s squared, where s represents the side length was used to solve this problem.
Taking the cube root of its volume will determine its side length.
Taking the cube root of its volume will determine its side length.
The side length is 4 cm.
The side length is 4 cm.
The side length is 8 cm.
. What can be concluded about the cube? Select the two that apply.(2 points)
Responses
The expression s2
, where s represents the side length was used to solve this problem.
The expression s squared, where s represents the side length was used to solve this problem.
Taking the cube root of its volume will determine its side length.
Taking the cube root of its volume will determine its side length.
The side length is 4 cm.
The side length is 4 cm.
The side length is 8 cm.
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To determine the correct conclusions about the cube with a volume of \( 64 \, \text{cm}^3 \), let's analyze the statements provided.
1. **Volume of a Cube**: The formula for the volume of a cube is given by \( V = s^3 \), where \( s \) is the side length of the cube.
2. **Finding the Side Length**: To find the side length, we take the cube root of the volume.
\[
s = \sqrt[3]{V} = \sqrt[3]{64 \, \text{cm}^3} = 4 \, \text{cm}
\]
Now we can evaluate the options:
1. **"The expression s², where s represents the side length was used to solve this problem."** - This statement is **false** because the volume relates to \( s^3 \), not \( s^2 \).
2. **"The expression s squared, where s represents the side length was used to solve this problem."** - This statement is also **false** for the same reason.
3. **"Taking the cube root of its volume will determine its side length."** - This statement is **true** as we used the cube root to find \( s \).
4. **"The side length is 4 cm."** - This statement is **true**, as we calculated \( s = 4 \, \text{cm} \).
5. **"The side length is 8 cm."** - This statement is **false** because, based on our calculation, the side length is not 8 cm.
Thus, the two correct conclusions from the options provided are:
- Taking the cube root of its volume will determine its side length.
- The side length is 4 cm.
1. **Volume of a Cube**: The formula for the volume of a cube is given by \( V = s^3 \), where \( s \) is the side length of the cube.
2. **Finding the Side Length**: To find the side length, we take the cube root of the volume.
\[
s = \sqrt[3]{V} = \sqrt[3]{64 \, \text{cm}^3} = 4 \, \text{cm}
\]
Now we can evaluate the options:
1. **"The expression s², where s represents the side length was used to solve this problem."** - This statement is **false** because the volume relates to \( s^3 \), not \( s^2 \).
2. **"The expression s squared, where s represents the side length was used to solve this problem."** - This statement is also **false** for the same reason.
3. **"Taking the cube root of its volume will determine its side length."** - This statement is **true** as we used the cube root to find \( s \).
4. **"The side length is 4 cm."** - This statement is **true**, as we calculated \( s = 4 \, \text{cm} \).
5. **"The side length is 8 cm."** - This statement is **false** because, based on our calculation, the side length is not 8 cm.
Thus, the two correct conclusions from the options provided are:
- Taking the cube root of its volume will determine its side length.
- The side length is 4 cm.
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