Volume by disk perpendicular to x axisFind the volume of the solid formed when region enclosed by y = x 1 / 2 , y = 6 − x, y = x 1 / 2 , y = 6 − x and y = 0 revolves around x axis.Can I use the equation for finding solids by splitting the solid into 2 parts?

Question

Volume by disk perpendicular to x axisFind the volume of the solid formed when region enclosed by   y  =      x          1              /            2        ,    y  =  6  −  x,   y  =      x          1              /            2        ,    y  =  6  −  x and   y  =  0 revolves around x axis.Can I use the equation for finding solids by splitting the solid into 2 parts?

Pignatpmv · Accepted Answer

Step 1  y  =      x          1              /            2        ,    y  =  6  −  x, so put       x          1              /            2        =  6  −  x.square both sides and get to       x    2    −  13  x  +  36  =  0solutions are 4 and 9, use   x  =  4 and   x  =  0 for the limits in the volume formula   V  =  ∫  π      y    2    d  x for curve   y  =      x          1              /            2      .Step 2Then similar for the line equation, between 4 and 6. Do separately then add.Draw a diagram to see the   x  =  6 point and why   x  =  4 was used, not   x  =  9.

jorgejasso85xvx · Accepted Answer

Explanation:To calculate area from known shapes   4  ⋅  2  ⋅            2      3        +  2  ⋅  2  ⋅            1      2

Find the volume of the solid formed when region enclosed by y=x^(1/2), y=6-x and y=0 revolves around x axis.

Answered question

Answer & Explanation

New Questions in High school geometry