The volume of the solid that results, when the region enclosed by the curves, is revolved about the x-axis is 3.35 cubic units.
What is a solid revolution?
When a figure is revolved around some fixed axis, the whole three-dimensional solid formed from the area that it swaps out is called a solid of revolution.
The function is given below.
y = - x² + 1
y = 0
Then the volume of the solid will be
[tex]\rm Volume = 2\int \pi y^2 dx\\\\\\Volume = 2 \int _0^1 \pi (-x^2 + 1)^2 dx\\\\\\Volume = 2 \pi \int _0^1 (x^4 - 2x^2 + 1)dx\\\\\\Volume = 2 \pi \left [ \dfrac{x^5}{5} - \dfrac{2x^3}{3} + x \right]^1_0\\\\\\[/tex]
On solving further, we have
Volume = 2π [(1/5 - 2/3 + 1) - 0]
Volume = 2π [8/15]
Volume = 3.35
Then the volume of the solid will be 3.35 cubic units.
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