Short Answer TypeThe volume of a spherical balloon is increasing at the rate of 25 cm3/sec. Find the rate of change of its surface area at the instant when its radius is 5 cm.
Long Answer TypeShort Answer TypeA ballon which always remains spherical on inflation, is being inflated by pumping in 900 cubic centimetres of gas per second. Find the rate of which the radius of the balloon is increasing when the radius is 15 cm.
The volume of a cube is increasing at a rate of 9 cubic centimeters per second. How fast is the surface area increasing when the length of an edge is 10 centimeters?
The volume of a cube is increasing at a rate of 7 cubic centimeters per second. How fast is the surface area increasing when the length of an edge is 12 centimeters?
The length x of a rectangle is decreasing at the rate of 2 cm/s and the width y is increasing at the rate of 2 cm/s. When x = 12 cm and y = 5 cm, find the rate of change of (a) the perimeter and (b) the area of the rectangle.
