A right circular cone of height h and base radius r has total surface area S consisting of its base area plus its side area, leading to the formula: Suppose you start out with a cone of height 8 cm and base radius 6 cm, and you want to change the dimensions in such a way that the total surface area remains the same. Suppose you increase the height by 5/100. In this problem, use tangent line approximation to estimate the new value of r so that the new cone has the same total surface area. The estimated value of r = 5.43 An elastic rope is attached to the ground at the positions shown in the picture. The rope is being pulled up along the dotted line. Assume the units are meters. 9 8 x ground level Assume that x is increasing at a rate of 7 meters/sec. (a) Write as a function of x: 0= (b) When x=10, the angle is changing at a rate of rad/sec. (c) Let L be the the left hand piece of rope and R the right hand piece of rope. When x=10, is the rate of change of L larger than the rate of change of R? ○ Yes ○ No