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Svetradugi [14.3K]
2 years ago
9

use the shell method to find the volume of the solid generated by revolving the region bounded by the given curves and lines abo

ut the y-axis. y=8-x^2,y=x^2,x=0
Mathematics
1 answer:
sukhopar [10]2 years ago
7 0

Answer:

16π square units.

Step-by-step explanation:

Please refer to the graph below.

So, if we draw a representative rectangle, the width of the rectangle will be (x), and the height of the rectangle at each (x) will be given by f(x) - g(x).

By the shell method:

\displaystyle V=2\pi\int_a^bp(x)h(x)\,dx

We are integrating from x = 0 to x = 2. p(x) is x and h(x) is f(x) - g(x):

\displaystyle V=2\pi\int_0^2(x)((8-x^2)-(x^2))\,dx

Evaluate. Simplify:

\displaystyle V=2\pi \int_0^2(8x-2x^3)\,dx

Hence:

\displaystyle V=2\pi\Big(4x^2-\frac{1}{2}x^4\Big|_{0}^{2}\Big)

Evaluate:

\displaystyle \begin{aligned} V &= 2 \pi \Big[(4(2)^2-\frac{1}{2}(2)^4)-(4(0)^2-\frac{1}{2}(0)^4)\Big]\\ &=2\pi(8) \\&=16\pi\text{ square units} \end{aligned}

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4.OA.2: The Turner family uses 548 liters of water per day. The Hill family uses 3 times as much water per day. How much more wa
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Well you can simplify them by dividing by there greatest common factor. 
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Soo..
36 ÷ 12 = 3 
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48 ÷ 12 = 4 

So your answer is 3/4!

Good Luck! :)
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3 years ago
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