Question

The trunk of a tree has diameter 30 cm. During the following year, the circumference grew 6 cm. 

(i) Approximately, how much did the tree’s diameter grow? 

(ii) What is the percentage increase in area of the tree’s cross-section?

Answer 1

(i) Given r = 15 cm and rate of change of perimeter = 6 cm 

To find the rate of change of diameter 

Now perimeter = p = 2πr

So dp = 2πdr 

Here dp = 6 cm (given)

So rate of change in diameter = d(2r) = 2dr = 2 x (3/π) = (6/π) cm 

(ii) A = πr2

Now dA = π(2r)dr

= 2πrdr