Answer:
C
Step-by-step explanation:
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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Answer:
The expected value of quarters is $47.20
Step-by-step explanation:
18+12+20=50
1230-50=1180
1180÷25=47.2
Answer:
2.65 feet
Step-by-step explanation:
Each revolution corresponds to a central angle of 2π radians, so 12 revolutions represent an arc of 24π radians. That means the arc length of 1 radian is ...
(1 rad)(200 ft)/(24π rad) ≈ 2.65 ft
The length of the arc with a central angle of 1 rad is about 2.65 feet.