Final answer:
To find the volume of the new cone, we first need to calculate the volume of the original cone, then use the given ratios to find the values for the radius and height of the new cone. Finally, we can calculate the volume of the new cone using the formula for the volume of a cone.
Step-by-step explanation:
To find the volume of the right circular cone with 2.5 times the radius and 7 times the height of cone A, we need to first find the volume of cone A. Given that the volume of cone A is 4 cubic meters, we can use the formula V = (1/3)πr²h to calculate the values of radius and height of cone A. Once we have the values for the radius and height of cone A, we can multiply them by the given ratios to find the values for the radius and height of the new cone. Finally, we can use the same formula V = (1/3)πr²h to calculate the volume of the new cone.
Let's calculate step-by-step:
1. Volume of cone A = 4 cubic meters
2. Use the formula V = (1/3)πr²h to calculate the values of r and h for cone A
3. Multiply r and h of cone A by 2.5 and 7 respectively to get the new values for the radius and height of the new cone
4. Use the formula V = (1/3)πr²h to calculate the volume of the new cone
Therefore, the volume, in cubic meters, of the right circular cone with 2.5 times the radius and 7 times the height of cone A is 70π cubic meters, so the correct answer is (a) 70π.