Homework Help: calculus ( related rates )

Posted by john on Wednesday, June 22, 2011 at 11:00am.

a paper cup in the shape of a cone has a diameter of 10cm across the top, and is 8cm deep. if the cup is leaking out the bottom at 2pi cm^3/min, at what rate is thet area of the water surface ( only the top surface of the water) changing, when the cup has a the water depth of 5cm? exact solutions first; round to two decimal places

calculus ( related rates ) - Reiny, Wednesday, June 22, 2011 at 12:39pm
Let the radius of the water level be r cm
let the height of the water be h cm
by ratios of similar triangles (using a cross-section)
r/h = 5/8 ----> h = 8r/5

V= (1/3)πr^2h
= (1/3)πr^2(8r/5) = (8π/15)r^3
dV/dt = (8π/5)r^2 dr/dt
-2π = (8π/5)r^2 dr/dt
when r = 5
dr/dt = -1/20

A =πr^2
dA/dt = 2πr dr/dt
when r = 5
dA/dt = 2π(5)(-1/20) = -π/2 cm^2/min

Answer this Question

Related Questions

Calculus(answer needed immediatly,thanks) - A paper cup has the shape of a cone...
Math - A cone shaped paper cup has a height of 7 inches and a diameter of 5 ...
Math - 2 part question 1) a cone shaped paper cup has a height of 7 inches and a...
Math ( Palette of Problem)s) - A cone shaped paper cup has a height of 7 inches ...
8th grade - Dimensions of a paper cup. The volume of a paper cup, shaped like a ...
CALCULUS - A cone shaped paper drinking cup is to be made from a circular piece ...
calculus - water in a paper conical filter drips into a cup. let x denote the ...
math - A cone shaped paper cup has a. Hight of 7 inches and a diameter of 5 ...
Calc - A paper cup is to be designed in the shape of a right circular cone. It ...
Math - A tank in the shape of a cone has a diameter of 8 feet and a height of 10...

For Further Reading

First Name:
School Subject:
Answer: