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14

Step-by-step Answer
PAGE: 186SET: ExercisesPROBLEM: 14
Please look in your text book for this problem Statement

(a)

The surface area of the snowball decreases at a rate of  cm2/min.

(b)

The rate at which diameter decreases when the diameter is 10 cm.

(c)

Diagram of the situation at any time .

The diameter of the snow ball is considered as .

(d)

Surface area of the sphere is .

Radius is half of the diameter .

Rewrite the surface area in terms of diameter .

Therefore, 

(e)

Consider .

Differentiate on each side with respect to .

The surface area of the snowball decreases at a rate of  cm2/min.

Thus, .

The rate at which diameter decreases when the diameter is 10 cm.

Thus,  cm.

Substitute  and   in equation (1).

The rate at which diameter decreases when the diameter is 10 cm is   cm/min.

(a)

The surface area of the snowball decreases at a rate of  cm2/min.

(b)

The rate at which diameter decreases when the diameter is 10 cm.

(c)

Diagram of the situation at any time  :

(d)

.

(e)

The rate at which diameter decreases when the diameter is 10 cm is cm/min.



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