Dipstick problems 395 Guided Project 20: Dipstick problem:s Topics and skills: I

Question

Dipstick problems 395 Guided Project 20: Dipstick problem:s Topics and skills: Integration, geometry, graphin,g Dipstick problems have a long and colorful history, much of which predates calculus. Around 1600 the Germarn astronomer and mathematician Johannes Kepler, while buying wine for his second wedding, questioned the method used for calculating the volume of wine in barrels, which involved inserting a measuring stick (dipstick) into the barrel. In 1735 the Scottish mathematician Colin Maclaurin wrote a paper to the government explaining how to use dipstick methods to measure the volume of molasses in large casks. In this project we consider a sequence of dipstick problems, some of which can be solved algebraically and some of which require calculus. In all that follows, we assume that the measuring stick is inserted vertically into the container Box-shaped tank Suppose that oil is stored in a closed box-shaped tank with a length of 3 m, a width of 2 m and a height of 4 m (Figure 1). On the top surface of the tank is a hole through which a measuring stick can be inserted vertically to measure the depth of oil in the tank. Assuming the tank rests horizontally on the ground, find the function V-J(h) that gives the volume of oil in the tank if the oil is h meters deep, where Oshs4. How much oil is in the tank if a depth of h 2.35 m is recorded? 1. 4 meters depth h 2 meters 3 meters Figure 1

Explanation / Answer

Since, the depth of the oil is h meters, the volume of the oil is

V(h)=length x width x depth of oil

=3 x 2 x h

=6h

Which is the required function for the volume of the oil.

Now, when the depth of the oil is h=2.35 m, the volume of the oil is

V(2.35)=6 x 2.35 =14.1 m^3

Related Questions

Navigate

• Browse (All)
• Browse D
• Subjects

---