Question
Question
Calculate the volume of a cylinder with a height of 25 millimeters and a diameter of 40 millimeters.(1 point)
Responses
1,000π mm3
1,000 pi mm cubed
40,000π mm3
40,000 pi mm cubed
4,000π mm3
4,000 pi mm cubed
10,000π mm3
Answers
GPT-4o mini
To calculate the volume of a cylinder, you can use the formula:
\[ V = \pi r^2 h \]
where \( V \) is the volume, \( r \) is the radius, and \( h \) is the height.
1. First, find the radius. The diameter is given as 40 millimeters, so the radius \( r \) will be:
\[ r = \frac{diameter}{2} = \frac{40 \, mm}{2} = 20 \, mm \]
2. Now plug the radius and height into the volume formula. The height \( h \) is given as 25 millimeters:
\[ V = \pi (20 \, mm)^2 (25 \, mm) \]
3. Calculate \( (20 \, mm)^2 \):
\[ (20 \, mm)^2 = 400 \, mm^2 \]
4. Now calculate the volume:
\[ V = \pi (400 \, mm^2)(25 \, mm) \]
\[ V = \pi (10,000 \, mm^3) \]
So, the volume is:
\[ V = 10,000 \pi \, mm^3 \]
Thus, the correct answer is:
**10,000π mm³** (or **10,000 pi mm cubed**).
\[ V = \pi r^2 h \]
where \( V \) is the volume, \( r \) is the radius, and \( h \) is the height.
1. First, find the radius. The diameter is given as 40 millimeters, so the radius \( r \) will be:
\[ r = \frac{diameter}{2} = \frac{40 \, mm}{2} = 20 \, mm \]
2. Now plug the radius and height into the volume formula. The height \( h \) is given as 25 millimeters:
\[ V = \pi (20 \, mm)^2 (25 \, mm) \]
3. Calculate \( (20 \, mm)^2 \):
\[ (20 \, mm)^2 = 400 \, mm^2 \]
4. Now calculate the volume:
\[ V = \pi (400 \, mm^2)(25 \, mm) \]
\[ V = \pi (10,000 \, mm^3) \]
So, the volume is:
\[ V = 10,000 \pi \, mm^3 \]
Thus, the correct answer is:
**10,000π mm³** (or **10,000 pi mm cubed**).