A tank that is in the form of an inverted cone contains liquid. The height h, in meters, of the space above the liquid is given by the formula h = 21 - 7/2r, where r is the radius of the liquid surface, in meters. The circumference of the top of the tank, in meters is...
(a) 9 pi
(b) 12 pi
(c) 15 pi
(d) 18 pi
(e) 21 pi
The answer says it is 12 pi but there is no solution, can some please explain?
When the height of the space above the liquid equals 0, the radius of the liquid's surface will be the same as the radius of the top of the tank.
So, plug in 0 for h and solve for r .
0 = 21 - \(\frac72\) r Add \(\frac72\)r to both sides of the equation.
\(\frac72\)r = 21 Multiply both sides of the equation by \(\frac27\) .
r = 6
This is the radius (in meters) of the liquid surface when there is no space above it, and so this is the radius of the top of the tank. So we have a circle with a radius of 6 meters.
circumference = 2pi * radius
circumference = 2pi * 6
circumference = 12pi