# Area for grazing by the goat tied to a silo

# Perimeter of the curve r = 4(1 + sin theta) by integration

# Length of Arc in Polar Plane | Applications of Integration

The length of arc on polar plane is given by the formula:

The formula above is derived in two ways. See it here: http://www.mathalino.com/reviewer/integral-calculus/length-arc-polar-pla...

# Length of Arc in XY-Plane | Applications of Integration

The length of arc in rectangular coordinates is given by the following formulas:

and

See the derivations here: http://www.mathalino.com/reviewer/integral-calculus/length-arc-xy-plane-...

# Longitude of an airplane crossing the equator

# Rate of change of surface area of sphere

**Problem**

Gas is escaping from a spherical balloon at the rate of 2 cm^{3}/min. Find the rate at which the surface area is decreasing, in cm^{2}/min, when the radius is 8 cm..

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