2 cos theta sin theta = cos theta
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The radius of the cylinder should be approximately 2.040 inches long.
<h3>How to calculate the radius of a rocket to contain a required quantity of powder</h3>
The volume required to store the powder is the sum of the volumes of the cylinder and the cone, whose expression is in this case:
204 in³ = (π/3) · r² · (4 in) + π · r² · h
204 in³ = (4/3 + h) · π · r²
204 in³ = (4/3 + 7 · r) · π · r²
204 = (4π/3) · r² + 7π · r³
7π · r³ + (4π/3) · r² - 204 = 0
The <em>positive</em> roots of the <em>cubic</em> equation are:
r ≈ 2.040 in
The radius of the cylinder should be approximately 2.040 inches long.
To learn more on volumes: brainly.com/question/1578538
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