The radius r of a circle is increasing at a rate of 7 centimeters per minute.

Question

Question

The radius r of a circle is increasing at a rate of 7 centimeters per minute. Find the rate of change of the area when r = 30 centimeters.

The radius r of a sphere is increasing at a rate of 4 inches per minute.

(a) Find the rate of change of the volume when r = 12 inches.

(b) Find the rate of change of the volume when r = 30 inches.

math calculus

Answer 1

✔ Recommended Answer

Answer #1

Answer 2

Similar Homework Help Questions

The radius r of a circle is increasing at a rate of 3 centimeters per minute.

The radius r of a circle is increasing at a rate of 3 centimeters per minute. Find the rate of change of the area when r = 39 centimeters.
The radius r of a sphere is increasing at a rate of 3 inches per minute.

The radius r of a sphere is increasing at a rate of 3 inches per minute. (a) Find the rate of change of the volume when r = 9 inches. (b) Find the rate of change of the volume when r = 36 inches.
A spherical balloon is inflated with gas at a rate of 900 cubic centimeters per minute....

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...

The height of a triangle is increasing at a rate of 1.5 centimeters/minute while the area of the triangle is increasing at a rate of 2.5 square centimeters per minute. At what rate is the base of the...

The height of a triangle is increasing at a rate of 1.5 centimeters/minute while the area of the triangle is increasing at a rate of 2.5 square centimeters per minute. At what rate is the base of the triangle changing when the height is 11 centimeters and the area is 92 square centimeters? Remember that you're using the formula for the area of a triangle: Area -bh (You'll need to know this formula in the normal homework assignments, quizzes and...
The radius of a sphere is increasing at a rate of 7.5 meters per minute. What...

The radius of a sphere is increasing at a rate of 7.5 meters per minute. What is the rate of change of the surface area of the sphere when the radius is 5 m (in square meters per minute)? Note that the surface area, S, of a sphere of radius ris S = 4xr? 330x m/min 100x mº/min 225x m/min 300x m/min 75x m/min
1) The Radiusp of a circle is Increasing At A Rate 6+1cm PER Minute. Find the...

1) The Radiusp of a circle is Increasing At A Rate 6+1cm PER Minute. Find the Rate of change of the Area when R=5

The radius r of a sphere is increasing at the uniform rate of 0.3 inches per second

The radius r of a sphere is increasing at the uniform rate of 0.3 inches per second. At the instant when the surface area S becomes 100pi square inches, what is the rate of increase, in cubic inches per second, in the volume V?
The radius of a right circular cone is increasing at a rate of 10 inches per...

The radius of a right circular cone is increasing at a rate of 10 inches per minute, and the height is decreasing at a rate of 4 inches per minute. What are the rates of change of the volume and the radius is 15 inches and the height is 45 inches? rate of change of the volume 13194.69 in3/min rate of change of the surface area 2402.85| in2/min
The altitude of a triangle is increasing at a rate of 1 centimeters/minute while the area...

The altitude of a triangle is increasing at a rate of 1 centimeters/minute while the area of the triangle is increasing at a rate of 2 square centimeters/minute. At what rate is the base of the triangle changing when the altitude is 8.5 centimeters and the area is 94 square centimeters? Preview cm/min

3. Suppose a forestfire spreads in a circle with radius changing at the rate of r(t)=0.2e10 feet per minute, the va...

3. Suppose a forestfire spreads in a circle with radius changing at the rate of r(t)=0.2e10 feet per minute, the variable t indicates the number of minutes since the fire started. At what rate is the area of the burning region increasing six hours after the fire started? Round your to nearest hundredth f(x)= of the burning region is increasing at a rate of ain units are clearly stated with your answer.) six hours after the fire started. 3. Suppose...