The surface area of the sphere is: A = 4 * pi * r ^ 2 Deriving we have: A '= 8 * pi * r * r' We clear the speed: r '= A' / (8 * pi * r) Substituting values: r '= 24 / (8 * pi * 3) r '= 1 / pi inch / sec Then, the volume of the sphere is: V = (4/3) * (pi) * (r ^ 3) Deriving we have: V '= (3) * (4/3) * (pi) * (r ^ 2) * (r') Substituting values: V '= (3) * (4/3) * (pi) * (3 ^ 2) * (1 / pi) Rewriting: V '= (4) * (9) V '= 36 inch3 / sec Answer: the volume of the ice is changing at 36 inch3 / sec at that moment
If the line is perpendicular, then its slope is the reciprocal of the given line's slope. This new line's slope is 1/2. We plug it into slope-intercept form
y = 1/2x + b
Now plug in the given point of (2, 10) and solve for b.
