Approximating changes Approximate the change in the lateral surface area (excluding the area of the base) of a right circular cone of fixed height of ?h? = 6 m when its radius decreases from ?r =10 m to ?r? = 9.9 m S = ?r ? + h .2

Solution 27E STEP 1 According to the approximation formula we can write f(x + x) f(x) = f(x).x f = f(x).x, Where f is the function,x is the variable and x is the change in x. STEP 2 Therefore according to this question, we have to approximate the change in the lateral surface area of a right circular cone of fixed height(h) and its radius(r) decreases from 10m to 9.9m. STEP 3 The lateral surface area of a right circular cone with radius r and height h is given by 2 2 S = r + h 2 2 r×2r 2 2 r (r +h +r) (2r +h ) S (r) = r + h + 2 2 = (r + h ) + 2 2 = 2 2 = 2 2 2r +h r +h r +h r +h Thus according to the equation ,we write S = S ().r......................(1) Here r=10 m and r = 9.9 10 = 0.1m Already given radius h=6m (1) (2r +h ) (2×10 +6 ) S = r = ( 0.1) = 236( 0.1) = 23.6m 3 r +h 10 +62 136 136 S = 23.6m3 136 23.6 3 Thus the change in S , S = 136m