Oops! That's the volume rotated about the x axis!
Volume rotated about the y axis is \(\int_0^9\pi x^2 dy \rightarrow \int_0^9 \pi ydy \rightarrow 81\pi/2\)
Volume of "disc" at x is \(\pi y^2dx\)
So overall volume = \(\int_0^3\pi x^4dx \rightarrow \pi 3^5/5 \rightarrow 243\pi/5\)
If the result is wanted in terms of d rather than theta then the following relationship can be used:
theta = cos-1(1 - 8d/D + 8d^2/D^2)
.
w = (Lcos(θ), Lsin(θ))
The area simplifies to A = (D^2/8)(theta - sin(theta))
The perimeter of the yellow segment is D(theta/2 + sin(theta/2)). The chord length can be found using either the cosine rule or the sine rule.
The description before A4 should read "Minimum L and Minimum W" of course!
"The side lengths of a rectangle have been measured to the nearest half of a meter as 7.5 and 18.5. What is the greatest possible percent error in finding the area of the rectangle?"
As follows:
"if S=-16p^2 + 160p represents the toatal sales for a company what is the highest sales this company can achieve?"
The following should help:
0.042 is correct for 4.2%, but 0.307 is 30.7%
Percent to decimal: divide by 100
Decimal to per cent: multiply by 100.
Old coordinates (x, y)
90 degree anti-clockwise rotation.
New coordinates (X, Y) = (-y, x)
+33665 
