Assume that the radius r of a sphere is expanding at a rate of 80 cm/min. The volume of a sphere is V = ar'and its surface area is 4rr. Determine the rate at which the surface area is changing with respect to time at t = 2 min, assuming that r = 10 at t = 0. (Use symbolic notation and fractions where needed.) dA cm-/min dt

Q: 2. Sand is being dropped at the rate of 10ft.3/min into a conical pile. If the height of the pile is…

A:

Q: The volume V of a cube with sides of length x in. is changing with respect to time. At a certain…

A: Given The volume V of a cube with sides of length x inch Side of the cube is 6inch that is x=6 inch…

Q: The radius of a right circular cone is increasing at a rate of 1.2 in/s while its height is…

A: Differentiate volume wrt t

Q: 2. A spherical snowball melts at a rate of 367T in /sec. At what rate is the radius of the snowball…

A:

Q: 2. The radius R of a circle is increasing at the rate of 1cm per sec. how fast is the area changing…

A: To find: The rate of change of area when . Formula used: Area of circle having radius R.…

Q: The ice cream in a sugar cone (conically shaped) has all melted and is dripping out a hole in the…

A: To express r in terms of h, use the the ratio between the height and radius of the cone is constant…

Q: A spherical balloon is inflating at a rate of 277T in³/sec. How fast is the radius of the balloon…

A:

Q: The volume of a cube decreases at a rate.1 of 15 m/sec. Find the rate at which the side of the cube…

A: It is given that the volume of a cube is decreasing at a rate of 15 m/sec. It is known that volume…

Q: A vertical cylinder is leaking water at a rate of 3 m/sec. If the cylinder has a height of 10 m and…

A: The volume of the cylinder is given by V=πr2h, where V=volume of the cylinder r=radius of the…

Q: A pebble is dropped into a calm pond, causing ripples in the form of concentric circles. The radius…

A: Rate of Radius of outer ripple increasing = 1 ft/sec                    Radius = 4 feet

Q: The radius of a spherical balloon is decreasing at a rate of in/sec.

A: Radius of balloon = r = 4 inchesDecreasing rate of balloon = drdt = -2πinches/secondVolume of…

Q: A cylindrical tank with radius 5 m is being filled with water at a rate of 3 m°, Imin: How fast 1.…

A:

Q: The depth of water in a 4m diameter cylindrical tank is increasing at the rate 0.7m/min. Find the…

A:

Q: A cube’s surface area increases at the rate of 72 in2/sec. At what rate is the cube’s volume…

A: Given:

Q: The volume of a cone of radius r and height h is given by V=1/3pir^2h. If the radius increases at a…

A: Volume of a cone = πr2h3 , Where r= radius of a cone and h= height of a conedrdt= 0.5cm/sec , dhdt=…

Q: The volume of a metal in a hollow spherical is constant. If the inner radius is increasing at thr…

A:

Q: m Oil is running into an inverted conical tank at the rate of 37 -. If the min tank has a radius 2.5…

A:

Q: The radius of a spherical ball is increasing at a rate of 2 cm/min. At exactly what rate (in…

A:

Q: Consider a pool shaped like the bottom half of a sphere, that is being filled. The radius of the…

A: The volume of hemisphere filled with liquid to height h = πrh2-π3h3

Q: The radius of an bubble is increasing at the rate of 1/2 cm/s. At what rate is the volume of the…

A: Here  radius of bubble is given and rate of change of radius of bubble is also given

Q: Assume that the radius r of a sphere is expanding at a rate of 70 cm/min. The volume of a sphere is…

A: Given Data: The rate of increase in radius is: drdt=70 cm/min The volume of the sphere is: V=43πr3…

Q: The volume V of a cube with sides of length x in. is changing with respect to time. At a certain…

A: Solved below

Q: Suppose a spherical balloon grows in such a way that after t seconds, its volume V is given by V = 4…

A:

Q: The radius of a sphere is increasing at the rate of 2 meters per se of change of the volume with…

A: Given: The radius of a sphere is increasing at the rate of 2 meters per second.

Q: Suppose a spherical balloon grows in such a way that after t seconds, its volume V is given by V = 4…

A:

Q: Assume that the radius r of a sphere is expanding at a rate of 80 cm/min. The volume of a sphere is…

A:

Q: A potter forms a piece of clay into a right circular cylinder. As she rolls it, the height h of the…

A: Here, given that the volume is constant. So, dVdt=0⇒ddtπr2h=0⇒πh 2rdrdt+r2dhdt=0⇒h 2rdrdt+r2dhdt=0…

Q: The original 24 m edge length x of a cube decreases at the rate of 2 m/min. a. When x = 1 m, at what…

A:

Q: The surface area of a sphere, initially zero, increases uniformly at 4 square inches pe second. Find…

A: Since you have asked multiple questions here, we will solve the first question for you. To get the…

Q: A flag is raised vertically from a pole at a constant rate of 1m/s. A point B on the ground level…

A: Given: Vertically raising speed of flag at constant rate=1 m/s……1Horizontal distance from flagpole…

Q: A spherical snowball is melting. Its radius decreases at a constant rate of 2 cm per minute from an…

A: Differentiation is the rate of change of some variable with respect to the other variable. If a…

Q: A mothball loses volume by evaporation at a rate proportional to its instantaneous area. If the…

A:

Q: A spherical balloon is inflated so that its radius (r) increases at a rate of 1/3cm/sec. How fast is…

A: Vloume(V)=43πr3Differentiate w.r.t tdVdt=43π.3r2.drdt

Q: Air is pumped into a spherical balloon so that its volume increases at a rate of 100 cm /s. How fast…

A: d[r^n]/dr = n r^(n-1)

Q: The radius of a spherical ball is increasing at a rate of 2 cm/min. At exactly what rate (in…

A: Given :radius of spherical ball is increasing at a rate of 2cm/minso, drdt=2cm/min

Q: A spherical snowball is melting in such a way that its surface area decreases at the rate of 1…

A:

Q: Use the differential dV to estimate the change in volume of a cube when the side length changes from…

A: We need to use the formula for differential to estimate the change in volume when side of the cube…

Q: How fast is the volume of a cube changing when the edge is 15 cm if the edge is changing at the rate…

A:

Q: A cube is expanding in such a way that the length of its diagonal is increasing at a rate of 5…

A: Let y be the diagonal, x be the length of an edge and V be the volume of the cube at any time t.…

Q: The radius of a sphere, initially zero, increases at the rate of 6ft per sec. Find how fast the…

A:

Q: Assume that the radius r of a sphere is expanding at a rate of 10in./min. The volume of a sphere is…

A:

Q: The area A(t) of a circular shape is growing at a constant rate. If the area increases from 97 to…

A:

Q: A spherical balloon is being filled with air at the constant rate of 2 cm³ How fast is the radius…

A: Given that The spherical balloon is being filled with air at constant rate of 2cm3/sec. Since the…

Q: A spherical balloon has a radius r that is increasing at a rate of 3 emfs. At what rate is the…

A: Given: drdt=3πcm/s   To find: dvdt when r=10

Q: How fast is the surface area of a cu

A: Given that : Edge of a cube = 30 cm Th edge changing at the rate of 3 mm per second.

Q: Suppose a snowball remains spherical while it melts, with the radius r shrinking at 3 inch(es) per…

A: Given: The radius of the spherical snowball is shrinking 3 inches in a hour.To find the numerical…

Q: 2. The diagonal of a square increases at the rate of 3 m/sec. How fast is the area changing when the…

A: Let the length of diagonal be y. so that, Now, Length of the side of a square be x. Using the…