The radius of a circle is changing at the rate of -2/pai  m/sec. At what rate is the circle’s area changing when r = 10 m?

Q: A spherical snowball melts at a rate of 36π^2in³/sec. At what rate is the radius of the snowball…

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Q: A 13-foot ladder rests against a vertical wall. If the bottom of the ladder slides away from the…

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

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Q: A spherical balloon is inflated with air at a rate of 32 cm3/ min. At what rate does the radius…

A: Find dr/dr.

Q: Find the rate at which the surface area of the water changes when the water is 10 ft high if the…

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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: The radius of a balloon is increasing at the rate of 10 cm / sec. At what rate is the surface area…

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Q: A ladder 15 ft long leans against a vertical wall. If the top slides down at the rate of 2 ft per…

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Q: What is the rate of change of the area of acircle (A = pai r2) with respect to the radius when the…

A: The radius of a circle is r=3 units. The formula for area of circle is given by A=πr2

Q: A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the…

A: To find: The rate at which the angle between the ladder and the ground  is changing

Q: Each side of a square is increasing at a rate of 6 cm/s. At what is the area of the square…

A: Given that, Area of square is  25cm2    Area A = x2 Where x is the side length. The area of square…

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

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Q: The radius r of a circle is changing at the rate of -2/π m/sec. At what rate is the circle’s area…

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

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Q: Rain is falling into a cylindrical barrel at the rate of 20 cm3/min. If the radius of the base is 18…

A: Given,            Rain is falling into a cylindrical barrel at the rate of 20 cm3/min.…

Q: The surface area of a sphere increases at a rate of 55 m²/sec. Then the rate at which the radius…

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Q: As a circular metal griddle is being heated, its diameter changes at a rate of 0.01 cm/min. Find the…

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Q: What is the velocity (in ft/s) of a sandbag 2.5 s after it is released from a hot-air balloon that…

A: Given that a sandbag is released from a hot-air balloon that is stationary in the air. Then we have…

Q: A car is slowing down at the rate 0.8 ft/sec². How far will the car move before it stops if its…

A:

Q: A 15-foot ladder is leaning against a mango tree. If the top of the ladder is sliding down the tree…

A: We need to find rate of bottom of ladder moving.

Q: A 10 ft ladder leans against a wall. If the top of the ladder slides down the wall at a rate of 2…

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Q: A 15-meter ladder is resting against a vertical wall, If the bottom of the ladder is being pushed…

A: Let ladder AB, l=15 m, Ladder is pushed horizontally at the rate of 1.5 m/s, ⇒dydt=1.5 We need to…

Q: How fast is the surface area of a circular oil spill in the ocean changing when the radius is 10ft…

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Q: The radius of a sphere decreases at a rate of 3 meters per second. Find the rate at which the…

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Q: A vertical cylinder is leaking water at a rate of 8m^3/sec. if the cylinder has a height of 10m and…

A: In a vertical cylinder water is leaking at a rate of 8 m3/sec. dVdt=8 Height of the cylinder is 10…

Q: The radius of a circle is increasing at the rate of 0.7 cm/sec.what is the rate of increase of its…

A: The radius of a circle is increasing at the rate drdt= 0.7 cm/sec r = radius of the circle

Q: Rain is falling into a cylindrical barrel at the rate of 20 cm3 /min. If the radius of the base is…

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Q: The radius of a circle is changing atthe rate of -2/paiA m/sec. At what rate is the circle’s area…

A: Let the radius of the circle be r. Then the area (A) of the circle is: A=πr2 Differentiating with…

Q: The radius of a circle is increasing at a rate of 5 centimeters per minute. Find the rate of change…

A: We can find the answer as below using the given data.

Q: ow fast is the radius changing when the diameter of the balloon is 50 cm?

A: Given: A spherical balloon is inflated at a rate of 1000 cm3 /sec . Diameter of the balloon = 50 cm

Q: A yellow balloon, spherical in shape is inflated with a rate of 100 cm3 /sec. Calculate the rate at…

A: Given

Q: A car is moving at 60 mi/hr (88 ft/sec) on a straight road when the driver steps on the brake pedal…

A: Given  Initial speed of the car =60 mi/hr (88 ft/sec) deceleration =12 ft/sec^2  time =3 sec

Q: A cube's volume increases at a rate of 108 ft3/min. At what rate is the cube's edge length changing…

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Q: A 35-ft ladder is leaning against a wall. If the bottom is pulled away from the wall at a rate of 8…

A: Let BC = x = distance from the base of wall to bottom of the ladderAB = y = distance from the base…

Q: A spherical balloon is being inflated at a rate of 9(pi)cm^3/sec. At what rate is its radius…

A:

Q: A 13-ft ladder is leaning against a house when itsbase starts to slide away. By the time thebase is…

A: If a ladder is leaning against a wall and when its base starts to slide away it makes a triangle…

Q: A conical cistern of height 5 ft and 7 ft across the top is being filled at a rate of 5 ft3/s while…

A: A conical cistern is given whose height is 5 ft and diameter at the top is 7 ft. A conical cistern…

Q: A kite 100ft  above the ground moves horizontally at a speed of 8ft/s  At what rate is the angle…

A: Let x= horizontal distance L= length of string,  Then a rough sketch of the problem is as follows:

Q: an oil spill is spreading in a circle at a rate of 316.7in/sec2. at what rate is the radius changing…

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Q: a 5-ft tall person walks away from a 20-ft tall streetlamp at a constant rate of 3 ft/s . at which…

A: Let us denote: x= distance of the person from the post y=length of the shadow Given that, dx/dt=3 ,…

Q: The sides of a square increases in length at a rate of 3 m/sec. At what rate is the area of the…

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Q: A conical cup is 4 cm across and 6 cm deep. Water leaks out of the bottom at the rate of 2 cm3 /sec.…

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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 rock is thrown from the top of a 120ft cliff with an initial velocity of 20 ft./sec  how 2…

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Q: A hot air balloon rising straight up from a level field is tracked by a range finder 500 ft from the…

A: Explained below

Q: An angler has a fish at the end of a line. The line is reeled in at 2 ft/sec from a bridge 30 feet…

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Q: . A kite 100 ft above the ground moves horizontally at aspeed of 8 fts. At what rate is the angle…

A: At what rate is the angle between the stringand the horizontal decreasing when 200 ft of string has…