A string is fit snugly around the circumference of a spherical hot
air balloon. More hot air is added (probably by a prominent scientist’s
lecture) and it now takes an additional 12.4 feet of string to fit
around the circumference. What is the increase in diameter?
can you give us the solution
To find the increase in diameter, we need to first determine the original diameter and the new diameter of the hot air balloon.
1. Let's assume the original diameter of the hot air balloon is D (in feet).
2. The original circumference of the balloon can be calculated using the formula: C = π * D, where π is approximately 3.14159.
3. As mentioned in the question, it takes an additional 12.4 feet of string to fit around the increased circumference.
4. So, the new circumference of the balloon is C + 12.4 feet.
5. Using the same formula for circumference, we have: C + 12.4 = π * d, where d is the new diameter we are trying to find.
6. Rearranging the equation, we get: d = (C + 12.4) / π.
Now we can plug in the values and calculate the increase in diameter.
Let's assume π is rounded to 3.14 for simplicity.
1. Suppose the original diameter D is x feet.
2. The original circumference C would be π * x.
3. The new diameter d can be calculated as: d = (C + 12.4) / π = (π * x + 12.4) / π = (3.14 * x + 12.4) / 3.14 = (3.14x + 12.4) / 3.14.
4. The increase in diameter is the difference between the new diameter d and the original diameter D: d - D = (3.14x + 12.4) / 3.14 - x.
By substituting the original diameter value, you can calculate the increase in diameter.