A spherical balloon is being inflated. Find the rate of increase of the surface areas with...
6) 7 marks A spherical balloon is being inflated. Using limit theory only: a) Find the instantaneous rate of change of its surface area (SA = 4nr2) with respect to its radius r when r = 10cm b) At another time, the instantaneous rate of change is 481 cm2/cm. What is the Surface Area of the balloon at this time?
A spherical balloon is inflated so that its volume is increasing at the rate of 3 ft 3/min. How fast is the radius of the balloon increasing when the radius is 1 ft?
4. A spherical balloon is inflated at a rate of 10 cubic feet per minute. How fast is the radius changing when the radius is 2 ft? (V = far)
A balloon is being inflated so that its volume is increasing at a constant rate of 200 c.c. per second. How fast is the radius increasing when the radius is 15 cm? Note that the volume is given by v=(4/3)π r^3.
A spherical balloon is inflated so that its volume is increasing at the rate of 2 ft3/min How rapidly is the diameter of the balloon increasing when the diameter is 1.3 feet? The diameter is increasing at _______ ft/min
A spherical balloon is inflated with gas at a rate of 900 cubic centimeters per minute. (a) Find the rates of change of the radius when r = 40 centimeters and r = 75 centimeters. r = 40 cm/min r = 75 cm/min (b) Explain why the rate of change of the radius of the sphere is not constant even though dV/dt is constant. The rate of change of the radius is a linear relationship whose slope is dV dt...
3.9 1. Balloons A spherical balloon is inflated and its volume increases at a rate of 15 in/min. What is the rate of change of its radius when the radius is 10 in? 2. Ladder against the wall A 13-foot ladder is leaning against a vertical wall (see figure) when Jack begins pulling the foot of the ladder away from the wall at a rate of 0.5 ft/s. How fast is the top of the ladder sliding down the wall...
Find the average surface area of a spherical balloon when the radius changes from r = 4 to r = 4.05 cm. The surface area formula for a sphere with radius r is A = 4πr^2 . Round to two decimal places.
A spherical rubber balloon carries a total charge Qdistributed uniformly over its surface. At t=0, the radius of the balloon is R. The balloon is then slowly inflated until its radius reaches 2R at the time t0.Determine the electric field due to this charge as a function of time (a) at the surface of the balloon, (b) at the surface of radius R, and (c) at the surface of radius 2R. Ignore any effect on the electric field due to the material of the balloon and...
A spherical balloon is inflating with helium at a rate of 641 it? min How fast is the balloon's radius increasing at the instant the radius is 2 ft? Write an equation relating the volume of a sphere, V, and the radius of the sphere, r. (Type an exact answer, using a as needed.) Differentiate both sides of the equation with respect to t. dv dr dt (Type an exact answer, using a as needed. Type an expression using r...