Question

The radius of a circular cylinder is increasing at rate of 3 cm/s while the height...

The radius of a circular cylinder is increasing at rate of 3 cm/s while the height is decreasing at a rate of 4 cm/s.

a.) How fast is the surface area of the cylinder changing when the radius is 11 cm and the height is 7 cm? (use A =2 pi r2 +2 pi rh )

b.) Based on your work and answer from part (a),is the surface area increasing or decreasing at the same moment in time? How do you know?

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Let V be the volume of a cylinder having height h and radius r, and assume...
Let V be the volume of a cylinder having height h and radius r, and assume that h and r vary with time. (a) How are dV /dt, dh/dt, and dr/dt related? (b) At a certain instant, the height is 18 cm and increasing at 3 cm/s, while the radius is 30 cm and decreasing at 3 cm/s. How fast is the volume changing at that instant? Is the volume increasing or decreasing at that instant?
The radius of a cylinder is increasing at a rate of 3cm/min while the height is...
The radius of a cylinder is increasing at a rate of 3cm/min while the height is decreasing at a rate of 10cm/min. What is the rate of change of the volume of the cylinder when the height is 100cm and the radius is 20cm? Please solve the question step by step
The side x of a rectangle is increasing at a rate of 2 cm/s while its...
The side x of a rectangle is increasing at a rate of 2 cm/s while its side y is decreasing at a rate of 1 cm/s. (a) Find how fast the perimeter P of the rectangle is changing when x = 4 cm and y = 3 cm. (b) Find how fast the area A of the rectangle is changing when x = 4 cm and y = 3 cm. (c) Find how fast the length l of diagonal of...
The altitude (height) of a triangle is increasing at a rate of 1 cm/min while the...
The altitude (height) of a triangle is increasing at a rate of 1 cm/min while the area of the triangle is increasing at a rate of 2 square cm per min. At what rate is the base of the triangle changing when the altitude is 10 cm and the area is 100 square cm?
10. A circular cylinder with a radius R of 1 cm and a height H of...
10. A circular cylinder with a radius R of 1 cm and a height H of 2 cm carries a charge density of ρV = H r2 sin φ µC/cm3 (r is a point on the z-axis, φ is an azimuthal angle). The cylinder is then placed on the xy plane with its axis the same as the z-axis. Find the electric field intensity E and the electric potential V on point A on z-axis 2 cm from the top...
The radius of a right circular cone is decreasing at a rate of 1.5cm/sec and the...
The radius of a right circular cone is decreasing at a rate of 1.5cm/sec and the height is increasing at a rate of 5cm/sec. At what rate is the volume changing when the height is 12cm and the radius 2cm? Leave your answer in terms of pi.
The height of a triangle is decreasing at a rate of 1 cm/min while its area...
The height of a triangle is decreasing at a rate of 1 cm/min while its area is increasing at a rate of 2 cm^2/min. (a) What is the base of the triangle when its height is 10 cm and its area is 100 cm^2? (b) At what rate is the base of the triangle changing when its height is 10 cm and its area is 100cm^2?
The volume of a right circular cylinder is given by V= πr2h, where r is the...
The volume of a right circular cylinder is given by V= πr2h, where r is the radius of its circular base and h is its height. Differentiate the volume formula with respect to t to determine an equation relating the rates of change dV/dt , dr/dt , dh/dt.   At a certain instant, the height is 6 inches and increasing at 1 in/sec and the radius is 10 inches and decreasing at 1 in/sec. How fast is the volume changing at...
The altitude (i.e., height) of a triangle is increasing at a rate of 1.5 cm/minute while...
The altitude (i.e., height) of a triangle is increasing at a rate of 1.5 cm/minute while the area of the triangle is increasing at a rate of 2.5 square cm/minute. At what rate is the base of the triangle changing when the altitude is 11.5 centimeters and the area is 87 square centimeters?
The altitude (i.e., height) of a triangle is increasing at a rate of 1.5 cm/minute while...
The altitude (i.e., height) of a triangle is increasing at a rate of 1.5 cm/minute while the area of the triangle is increasing at a rate of 2.5 square cm/minute. At what rate is the base of the triangle changing when the altitude is 10.5 centimeters and the area is 89 square centimeters?