In 1625 CE, a monument was found in Chang'an in China that records the history of the Christian religion in China. The monument dates from 781 CE. Christianity had its beginnings in Rome, which was almost 5,000 miles away. How might the monument have gotten there?
The volume of the solid that lies inside both the cylinder x² + y² = 1 and the sphere x² + y² + z² = 16 is 24.74 cubic units.
<h3>What is the volume of the solid?</h3>
Find the volume of the solid that lies inside both the cylinder x² + y² = 1 and the sphere x² + y² + z² = 16
From the sphere and cylinder, the cylindrical coordinate will be

And the radius of the cylinder is |r| < 1 and the 0 ≤ θ ≤ 2π.
Then the volume will be given as
![\rm V = \int _0^{2\pi} \int _0^1 \int _{- \sqrt{16 - r^2}}^{\sqrt{16-r^2}} \left ( r \ dz \ dr \ d\theta \right ) \\\\\\V = 2\pi \int_0^1 \left ( 2r\sqrt{16-r^2} \right ) \ dr\\\\\\V = 4\pi \left [ -\dfrac{1}{3} (16 - r^2)^{3/2} \right ]\\\\\\V = \dfrac{4\pi}{3} \left ( 16^{3/2} - 15^{3/2} \right )\\\\\\V = 24.74](https://tex.z-dn.net/?f=%5Crm%20V%20%3D%20%5Cint%20_0%5E%7B2%5Cpi%7D%20%5Cint%20_0%5E1%20%5Cint%20_%7B-%20%5Csqrt%7B16%20-%20r%5E2%7D%7D%5E%7B%5Csqrt%7B16-r%5E2%7D%7D%20%5Cleft%20%28%20r%20%5C%20dz%20%5C%20dr%20%5C%20d%5Ctheta%20%20%5Cright%20%29%20%5C%5C%5C%5C%5C%5CV%20%3D%202%5Cpi%20%5Cint_0%5E1%20%5Cleft%20%28%202r%5Csqrt%7B16-r%5E2%7D%20%5Cright%20%29%20%5C%20dr%5C%5C%5C%5C%5C%5CV%20%3D%204%5Cpi%20%5Cleft%20%5B%20-%5Cdfrac%7B1%7D%7B3%7D%20%2816%20-%20r%5E2%29%5E%7B3%2F2%7D%20%5Cright%20%5D%5C%5C%5C%5C%5C%5CV%20%3D%20%5Cdfrac%7B4%5Cpi%7D%7B3%7D%20%5Cleft%20%28%2016%5E%7B3%2F2%7D%20-%2015%5E%7B3%2F2%7D%20%5Cright%20%29%5C%5C%5C%5C%5C%5CV%20%3D%2024.74)
More about the volume of the solid link is given below.
brainly.com/question/23705404
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This question is solved using proportions, and doing this, it is found that Evan gets 5 Chinese yuans for every Australian dollar.
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- Evan budgeted $60 for the taxi ride.
- He went $15 over, thus, the taxi ride cost $75.
- In Chinese yuans, the cost was 375.
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75 dollars are worth 375 yuans. How much yuans is a dollar worth?
1 dollar - x yuans
75 dollars - 375 yuans
Applying cross multiplication:



Evan gets 5 Chinese yuans for every Australian dollar.
A similar question is given at brainly.com/question/23352001
Answer:
The axis of symmetry is x=1