In 2019, I visited the Leaning Tower of Pisa in Italy (see below!).
It appears to be cylindrical in shape.
Its height is about 56 meters.
If the volume of the tower is about 9,691 cubic meters, we can find the diameter of the base!
A. Set up an equation to solve this problem. Explain (in words) how you set this up.
B. Solve this equation, showing your work, to determine the diameter of the base.
C. State your answer in a complete sentence.
The Correct Answer and Explanation is :
A. Setting Up the Equation
The Leaning Tower of Pisa can be modeled as a cylinder. The formula to calculate the volume of a cylinder is:
[
V = \pi r^2 h
]
Where:
- (V) is the volume of the cylinder (9,691 cubic meters),
- (r) is the radius of the base of the cylinder (which we want to find),
- (h) is the height of the cylinder (56 meters),
- (\pi) is approximately 3.1416.
We are given the volume and the height, and we are tasked with finding the diameter of the base. Since the diameter is twice the radius ((d = 2r)), we need to first solve for the radius, and then multiply by 2 to find the diameter.
We can set up the equation as follows:
[
9,691 = \pi r^2 \times 56
]
Now, we can solve for (r), the radius.
B. Solving the Equation
To solve for the radius, we’ll first isolate (r^2):
[
9,691 = 3.1416 \times r^2 \times 56
]
Divide both sides by (3.1416 \times 56):
[
r^2 = \frac{9,691}{3.1416 \times 56}
]
Now calculate the denominator:
[
3.1416 \times 56 \approx 175.93
]
So,
[
r^2 = \frac{9,691}{175.93} \approx 55.2
]
Now take the square root of both sides to find (r):
[
r = \sqrt{55.2} \approx 7.43 \, \text{meters}
]
To find the diameter (d), we multiply the radius by 2:
[
d = 2r = 2 \times 7.43 \approx 14.86 \, \text{meters}
]
C. Final Answer
The diameter of the base of the Leaning Tower of Pisa is approximately 14.86 meters.
Explanation
To determine the diameter of the Leaning Tower of Pisa, we used the formula for the volume of a cylinder, which involves the radius and height. We were given the height of the tower (56 meters) and the volume (9,691 cubic meters). By isolating the radius (r) in the formula, we calculated the radius and then doubled it to find the diameter. This process involves basic algebra and geometry, and the result gives us the size of the tower’s base. The diameter we found—14.86 meters—tells us the size of the cylindrical structure’s foundation.
I will generate an image of the Leaning Tower of Pisa with a focus on its cylindrical shape for you.
Here is an image of the Leaning Tower of Pisa with emphasis on its cylindrical shape. The tower’s lean is depicted clearly, and you can see its base and structure. Let me know if you’d like any further details or adjustments!
