1) A street light is at the top of a 20 ft tall pole. A woman 6 ft tall walks aw

Question

1) A street light is at the top of a 20 ft tall pole. A woman 6 ft tall walks away from the pole with a speed of 5 ft/sec along a straight path. How fast is the tip of her shadow moving when she is 45 ft from the base of the pole?

Note: You should draw a picture of a right triangle with the vertical side representing the pole, and the other end of the hypotenuse representing the tip of the woman's shadow. Where does the woman fit into this picture? Label her position as a variable, and label the tip of her shadow as another variable. You might like to use similar triangles to find a relationship between these two variables.

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2) The radius of a spherical balloon is increasing at a rate of 3 centimeters per minute. How fast is the surface area changing when the radius is 8 centimeters?

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3) Gravel is being dumped from a conveyor belt at a rate of 20 cubic feet per minute. It forms a pile in the shape of a right circular cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is 14 feet high?

Recall that the volume of a right circular cone with height h and radius of the base r is given by

Note: See number 23 on pg 261 for a picture of this.

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Explanation / Answer

Volume of a cone = (1/3)?r

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