Calculator Technique For Solving Volume Flow Rate Problems In Calculus

Calculator Technique for Solving Volume Flow Rate Problems in Calculus The following models of CASIO calculator may work with this method: fx-570ES, fx-570ES Plus, fx115ES, fx-115ES Plus, fx-991ES, and fx-991ES Plus. The following calculator keys will be used for the solution

Name

Key

Operation

Name

Key

Operation

Shift

SHIFT

Stat

SHIFT → 1[STAT]

Mode

MODE

AC

AC

This is one of the series of post in calculator techniques in solving problems. You may also be interested in my previous posts: Calculator technique for progression problems and Calculator technique for clock problems; both in Algebra. Flow Rate Problem Water is poured into a conical tank at the rate of 2.15 cubic meters per minute. The tank is 8 meters in diameter across the top and 10 meters high. How fast the water level rising when the water stands 3.5 meters deep. Traditional Solution

Volume of water inside the tank

Differentiate both sides with respect to time

When h = 3.5 m

answer Solution by Calculator ShowClick here to show or hide the concept behind this technique MODE → 3:STAT → 3:_+cX2

X 0 10 5

Y 0 π42 π22

AC → 2.15 ÷ 3.5y-caret = 0.3492

answer

To input the 3.5y-caret above, do 3.5 → SHIFT → 1[STAT] → 7:Reg → 6:y-caret

What we just did was actually v = Q / A which is the equivalent of

for this problem.

Problem Water is being poured into a hemispherical bowl of radius 6 inches at the rate of x cubic inches per second. Find x if the water level is rising at 0.1273 inch per second when it is 2 inches deep? Traditional Solution Volume of water inside the bowl

Differentiate both sides with respect to time

When h = 2 inches, dh/dt = 0.1273 inch/sec

answer Calculator Technique MODE → 3:STAT → 3:_+cX2

X 0 6 12

Y 0 π62 0

AC → 0.1273 × 2y-caret = 7.9985

answer

I hope you enjoy this post. Next time you solve problems involving flow rate, try to use this calculator technique to save time. - See more at: http://www.mathalino.com/blog/romel-verterra/calculator-technique-solving-volumeflow-rate-problems-calculus#sthash.2gpn6ak5.dpuf