Approximating changes Approximate the change in the volume of a right circular cone of fixed height ?h =4m when its radius increases from ?r? =3 ?m? to ?r? = 3.05 m (?V?(?r?) = ??r?2 ?h?/3).

Solution 26E 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 volume(v) of a right circular cone of fixed height(h) and its radius(r) increases from 3m to 3.05m. STEP 3 The volume of a right circular cone with radius r and height h is given by 1 2 2 h v(r) = 3r h vr) = 3 Thus according to the equation ,we write v = v().r......................(1) Here r=3 m and r = 3.05 3 = 0.05m Already given radius h=4m (1) 2 2 1.2 3 3 v = 33)(4)(0.05) = ×30.6 = 3 m = 0.4 m v = 0.4 m 3 3 Thus the change in v , v = 0.4 m