This word problem is asking for a graph that shows your representative rectangle. Not sure how to set up this proof. No other information given :(
Please help
Please help
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Use a circle centre (0,0) and radius r.
Rotate this circle about the x axis to generate a sphere
The volume of a disk slice at distance x from the origin
= pi*y^2.dx
x^2+y^2 = r^2
y^2 = r^2 - x^2
Volume of disk
=pi*(r^2-x^2).dx
To get the volume of the whole sphere integrate
from x =-r to +r
V = integral pi*(r^2-x^2)dx from -r to +r
= pi*[xr^2-x^3/3] from -r to +r
=pi[ (r^3-r^3/3) -(-r^3 + r^3/3)]
= pi[2r^3-2r^3/3] = 4pi*r^3/3
Rotate this circle about the x axis to generate a sphere
The volume of a disk slice at distance x from the origin
= pi*y^2.dx
x^2+y^2 = r^2
y^2 = r^2 - x^2
Volume of disk
=pi*(r^2-x^2).dx
To get the volume of the whole sphere integrate
from x =-r to +r
V = integral pi*(r^2-x^2)dx from -r to +r
= pi*[xr^2-x^3/3] from -r to +r
=pi[ (r^3-r^3/3) -(-r^3 + r^3/3)]
= pi[2r^3-2r^3/3] = 4pi*r^3/3