Welcome to Westonci.ca, where your questions are met with accurate answers from a community of experts and enthusiasts. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.
Sagot :
Certainly! Let's solve this problem step-by-step.
1. Understand the volumes:
- The volume of a cylinder is calculated using the formula:
[tex]\[ V_{\text{cylinder}} = \pi r^2 h \][/tex]
where [tex]\( r \)[/tex] is the radius and [tex]\( h \)[/tex] is the height of the cylinder.
- The volume of a cone with the same radius and height is calculated using the formula:
[tex]\[ V_{\text{cone}} = \frac{1}{3} \pi r^2 h \][/tex]
2. Relationship between volumes:
- Notice from the formulas that the volume of a cone is exactly one-third the volume of a cylinder with the same radius and height.
3. Given data:
- We are given that the volume of the cylinder is [tex]\( 1200 \, \text{yd}^3 \)[/tex].
4. Calculate the volume of the cone:
Since the volume of the cone is one-third of the volume of the cylinder:
[tex]\[ V_{\text{cone}} = \frac{1}{3} \times V_{\text{cylinder}} \][/tex]
5. Substitute the given volume:
[tex]\[ V_{\text{cone}} = \frac{1}{3} \times 1200 \, \text{yd}^3 \][/tex]
6. Perform the arithmetic:
[tex]\[ V_{\text{cone}} = 400 \, \text{yd}^3 \][/tex]
So, the volume of the cone with the same radius and height as the cylinder is [tex]\( 400 \, \text{yd}^3 \)[/tex].
1. Understand the volumes:
- The volume of a cylinder is calculated using the formula:
[tex]\[ V_{\text{cylinder}} = \pi r^2 h \][/tex]
where [tex]\( r \)[/tex] is the radius and [tex]\( h \)[/tex] is the height of the cylinder.
- The volume of a cone with the same radius and height is calculated using the formula:
[tex]\[ V_{\text{cone}} = \frac{1}{3} \pi r^2 h \][/tex]
2. Relationship between volumes:
- Notice from the formulas that the volume of a cone is exactly one-third the volume of a cylinder with the same radius and height.
3. Given data:
- We are given that the volume of the cylinder is [tex]\( 1200 \, \text{yd}^3 \)[/tex].
4. Calculate the volume of the cone:
Since the volume of the cone is one-third of the volume of the cylinder:
[tex]\[ V_{\text{cone}} = \frac{1}{3} \times V_{\text{cylinder}} \][/tex]
5. Substitute the given volume:
[tex]\[ V_{\text{cone}} = \frac{1}{3} \times 1200 \, \text{yd}^3 \][/tex]
6. Perform the arithmetic:
[tex]\[ V_{\text{cone}} = 400 \, \text{yd}^3 \][/tex]
So, the volume of the cone with the same radius and height as the cylinder is [tex]\( 400 \, \text{yd}^3 \)[/tex].
Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.