The volume of the region R bounded by the x-axis is: 
<h3>What is the volume of the solid (R) on the X-axis?</h3>
If the axis of revolution is the boundary of the plane region and the cross-sections are parallel to the line of revolution, we may use the polar coordinate approach to calculate the volume of the solid.
From the given graph:
The given straight line passes through two points (0,0) and (2,8). Thus, the equation of the straight line becomes:

here:
- (x₁, y₁) and (x₂, y₂) are two points on the straight line
Suppose we assign (x₁, y₁) = (0, 0) and (x₂, y₂) = (2, 8) from the graph, we have:

y = 4x
Now, our region bounded by the three lines are:
Similarly, the change in polar coordinates is:
where;
- x² + y² = r² and dA = rdrdθ
Therefore;
- rsinθ = 0 i.e. r = 0 or θ = 0
- rcosθ = 2 i.e. r = 2/cosθ
- rsinθ = 4(rcosθ) ⇒ tan θ = 4; θ = tan⁻¹ (4)
- ⇒ r = 0 to r = 2/cosθ
- θ = 0 to θ = tan⁻¹ (4)
Then:


Learn more about the determining the volume of solids bounded by region R here:
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Answer:
In cold regions, such as the North Atlantic Ocean, ocean water loses heat to the atmosphere and becomes cold and dense. When ocean water freezes, forming sea ice, salt is left behind causing surrounding seawater to become saltier and denser. Dense-cold-salty water sinks to the ocean bottom.
Step-by-step explanation:
Answer: About 63 in²
Step-by-step explanation:
<u>Area of circle = π · r²</u>
- r = radius length
- π ≈ 3.14
<u>Area of large pizza:</u>

<u>Area of small pizza:</u>

<u>Difference in area:</u>
