To determine the radius of the soup can, we start with the information given:
1. The volume of the soup can (V) is 360 mL (since 1 mL is equivalent to 1 cm³, this is 360 cm³).
2. The height (h) of the can is 17 cm.
The formula for the volume of a cylinder is given by:
[tex]\[ V = \pi r^2 h \][/tex]
Where:
- [tex]\( V \)[/tex] is the volume
- [tex]\( r \)[/tex] is the radius
- [tex]\( h \)[/tex] is the height
- [tex]\( \pi \)[/tex] (pi) is a constant approximately equal to 3.14159
We need to solve for the radius [tex]\( r \)[/tex]. Rearrange the volume formula to isolate [tex]\( r \)[/tex]:
[tex]\[ r^2 = \frac{V}{\pi h} \][/tex]
Then, take the square root of both sides to solve for [tex]\( r \)[/tex]:
[tex]\[ r = \sqrt{\frac{V}{\pi h}} \][/tex]
Substitute the given values into the equation:
[tex]\[ r = \sqrt{\frac{360}{3.14159 \times 17}} \][/tex]
After evaluating the expression inside the square root and taking the square root, we obtain:
[tex]\[ r \approx 2.596281945921045 \][/tex]
Therefore, the radius of the soup can is approximately 2.60 cm.
Here is a diagram of the soup can for better understanding:
In this diagram:
- The height (h) is labeled as 17 cm.
- The radius (r) from the center to the side is labeled as approximately 2.60 cm.
- The entire volume of the can is 360 cm³.
The radius of the soup can is approximately 2.60 cm.
