An hemispherical dome is half a sphere. If the diameter is 60 m, then the radius is 30 m.
We can use differentials to solve this problem because we are adding a thin layer to the original dome, so the volume of the dome in increased by a differential of itself.
This differential volume that the dome is increased is equal to the volume of the coat of paint.
The volume of the dome can be written as:
Now, we can calculate dV as:
Answer: the paint needed for this coat is approximately 7.92 m^3
It was $21.93 and I need more letters to submit this
Answer: (3y) + 7+x
Step-by-step explanation:
You just flip and then their equivalent
<u>For this problem, we need to use our integral knowledge to set up the problem</u>:
<u>The bounds will be from 2 to 6, cutting tiny horizontal bars into the graph, to approximate the area</u>
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<u>Now for the function inside the integral</u>:
⇒ it is the <em>top function</em> minus the <em>bottom function</em>
- <em>top function: y= x²</em>
- <em>bottom function: x-axis ⇒ y =0</em>
<em> ⇒</em> <u>function within integral</u> = x² - 0
<u>Let's put it all together and solve</u>:
<u>Answer: 208/3 ≈ 69.333</u>
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Hope that helps!