Formula
What is (right circular) frustum?
What is 30pi?
Surface area can be though of arc length multiplied by this.
The length of the curve y = x for
0 < x < 1
What is sqrt2?
The formula for arc length on the Cartesian plane
What is sqrt(1 + (dy/dx)^2)?
The formula for the lateral surface area of a cone.
What is pi*r*l?
The lateral surface area of a pool noodle of length 5 with outer radius 3 and inner radius 2
What is 50pi?
True or false: there are multiple ways to represent arc length.
What is true?
The length of the curve y = sqrt(1-x^2) for
0 < x < 1
What is pi/4?
The formula for arc length using polar coordinates.
What is sqrt(r^2 + (r'(theta))^2)?
The formula for the lateral surface area of a frustum.
What is pi*(r1+r2)*l? (Or 2*pi*r*l)
What is sqrt2*pi?
True or false: the arc length of a function changes depending on what line you rotate it about. (Assume the bounds remain the same).
What is false?
The volume of a pool noodle with length 5, outer radius 3, and inner radius 2.
What is 25pi?
The formula you would use to rotate the function f(x) about the x-axis, for a < x < b
What is the integral from a to b of 2*pi*f(x)*sqrt(1 + (f'(x))^2) dx ?
2pi*r*l is the formula for surface area of these two 3d shapes, where r is the average radius and l is the (slant) height.
What is right circular frustum and cylinder?
The lateral surface area generated when the curve y = sqrt(1-x^2) is rotated about the y-axis, for 0 < x < 1.
What is 2pi?
Between arc length and volume, the answer is the one that is more similar to surface area. Please give a reason why.
What is arc length, because a) it is located directly in the surface area formula b) it behaves more similarly when multiple curves are involved c) it's used to find the figurative "height" of the surface.
The volume generated when the curve y = sqrt(1-x^2) is rotated about the y=axis, for 0 < x < 1.
What is the integral from g inverse of a to g inverse of b of 2*pi*y*sqrt(1+(g'(y))^2) dy?
The infinite Riemann sum representing the surface area of the curve f(x) rotated about the x-axis
What is the limit as n approaches infinity of the sum from i = 1 to i = n of 2*pi*f(xi)*sqrt(1+(f'(xi))2)*(change in x).
The lateral surface area, rounded to the nearest thousandth, generated when the curve y = x^2 is rotated about the x-axis for 0 < x < 2. (Calculator permitted).
What is 53.226?
The percent chance you get this problem correct.
What is 100%?
The exact volume generated when the curve y = x^2 is rotated about the x-axis for 0 < x < 2.
What is 32pi/5?