The volume of a cylinder varies jointly with the square of the radius and the height. if the volume of a cylinder is 50.265 cubic inches when the radius is 2 inches and the height is 4 inches, what is the volume when the radius is 3 inches and the height is 7 inches?

Just use the formula v = pi.(r^2).h that gives v = 9pi.7 that gives approximately 197.92 cubic inches.

We look for the equation of the line AB
 We have then:
 y-yo = m (x-x0)
 m = (y2-y1) / (x2-x1)
 m = (4 - (- 1)) / (4 - (- 3))
 m = 5/7
 We choose an ordered pair:
 (xo, yo) = (4, 4)
 Substituting:
 y-4 = (5/7) (x-4)
 y = (5/7) x-20/7 + 4
 7y = 5x - 20 + 28
 7y = 5x + 8
 y = (5/7) x + 8/7
 The equation of the perpendicular line is:
 -7x - 5y = -48
 
 the equation of BC is:
 (C) -7x - 5y = -48