Answer:
The volume is 25.1 cubic inches
Step-by-step explanation:
Given
--- base radius
--- height
Required
The volume (V) of the cylinder
This is calculated using:
So, we have:
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Given:
A circle with radius 7 units and chord CD = 7 units.
To find:
The measure of arc CD.
Solution:
Let O be the center of the circle.
In triangle OCD,
(Given)
(Radii of same circle)
(Given)
Since all sides are equal, therefore, the triangle OCD is an equilateral triangle.
Measure of each angle of an equilateral triangle is 60 degrees. So,
The measure of central angle is equal to the measure of corresponding arc.
Therefore, the measure of arc CD is 60 degrees.
Explanation:
The key to area in polar coordinates is the formula for the area of a sector:
a = (1/2)r²θ
Then a differential of area* can be written as ...
da = (1/2)r²·dθ
Filling in the given function for r, we have ...
da = (1/2)(4cos(3θ))²·dθ = 8cos(3θ)²·dθ
The integral will have limits corresponding to the range of values of θ for one loop of the graph: -π/6 to π/6. So, the area is ...
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* As with other approaches to finding area (horizontal or vertical slice, for example), we assume that the differential element dθ is sufficiently small that we need not concern ourselves with the fact that r is a function of θ.