When a circular plate of metal is heated in a oven, its radius increases at a rate of 0.05 cm/min. at what rate is the plate's area increasing when the radius is 52cm?

Q: If a snowball melts so that its surface area decreases at a rate of 1cm /min, find the rate at which…

A: Diameter= DRadius = r =D/2Surface area = A= 4pi*r^2Given dA/dt= -1 cm^2/min (negative because…

Q: each side of a square increases at a rate of 1.5cm/sec .also find the rate at which the area of the…

A: Given,   Each side of a square increases at a rate of 1.5 cm/sec

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

A:

Q: A Ferris wheel with a radius of 10 m is rotating at a rate of one revolution every 2 minutes. How…

A: the height is given byh = 10 sin (pi * t) + 10dh/dt = 10 cos (pi * t) * pi

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: Sugar is poured into a conical tank at the rate of 15cm3/sec whose bottom radius is always quarter…

A: The volume of a cone is given by the formula V=13πr2h. Where, V-volume, r-radius and h is the height…

Q: A 6-ft tall man is walking away from a 15-ft tall street lamp at the rate of 5 ft/sec. How fast is…

A: Here we find rate of shadow lengthening.

Q: A stone dropped into a still pond sends out a circular ripple whose radius increases at a constant…

A:

Q: A stone dropped into a still pond sends out a circular ripple whose enclosed area increases at a…

A:

Q: A picture 40cm high is placed on a wall with its base 30cm above the level of the eye of an…

A: Shown below

Q: At what rate is water pouring into a rectangular bathtub with base 65 fť if the water level rises at…

A: According to the given information it is required to calculate the rate at which water is pouring…

Q: A stone dropped in a pond sends out a circular ripple whose radius increases at a constant rate of 3…

A: Given that:Rate of increase of radius, drdt=3 ft/s

Q: Suppose the radius of a sphere is increasing at a rate of 5 in/second.  At what rate is the surface…

A: Given that radius of a sphere is increasing at an of 5 in/sec. Let r be the initial radius of the…

Q: The sides of a square increase in length at a rate of 5 m/sec. a. At what rate is the area of the…

A: We apply chain rule of differentiation. Area of the square is: A= s2.  Where s is the side of a…

Q: The volume of a cube is increasing at the rate of 21 cc/min. At what rate is its surface area…

A: The volume of a cube is increasing at rate, dVdt = 21 cc/min To evaluate: The rate at which the…

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 width of a rectangle is increasing at a rate of 2 cm/sec, while the length increases at 3…

A: The rate of increase of the width of a rectangle i.e. dwdt=2 cm/sec The rate of increase of the…

Q: A spherical balloon is being deflated at a rate of 80 cm3/min. At what rate is the radius decreasing…

A:

Q: If a snowball melts so that its surface area decreases at a rate of 2 cm2/min, find the rate at…

A:

Q: When a circular plate of metal is heated in an​ oven, its radius increases at a rate of 0.04…

A: When a circular plate of metal is heated in an​ oven, its radius increases at a rate of  0.04…

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

A:

Q: A snowball is melting at a rate of 2.4ft^3 hr^-1 – if the snowball remains a sphere throughout the…

A: given: A snowball is melting at a rate of 2.4ft3/hr. that implies dVdt=-2.4ft3/hr where V is the…

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

A:

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

A:

Q: The volume of a cube is increasing at the rate of 8 cm /sec.How fast is the surface area in creasing…

A: We can find the answer as below

Q: A spherical balloon is inflated at a rate of 10 cm3>min. At what rate is the diameter of the…

A:

Q: 2) A person is standing 350 feet away from a model rocket that is fired straight up into the air at…

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

A: let the side of the square is a meter, and the area is A given that da/dt=3m/sec a. a=15m area of…

Q: A Ferris wheel with a radius of 13m is rotating at a rate of one revolution every 2 minutes. How…

A: Given thatRadius of the Ferris wheel is 13 mThe time period of the Ferries wheel is 2 min To find…

Q: If a snowball melts so that its surface area decreases at a rate of 1 cm²/min, find the rate at…

A: 1) Let A be the surface area  r = radius of the sphere D = diameter of sphere = 10 cm…

Q: A 100-ft long cable of diameter 4 in. is subsequently submerged in seawater. Due to corrosion, the…

A: Given that diameter is 4 inches and height is 100 feet. And rate of decrease in area is 750 in2yr.…

Q: A stone dropped into a still pond sends out a circular ripple whose radius increases at a constant…

A: Given: A stone dropped into a still pond sends out a circular ripple whose radius increases at a…

Q: at a certain instant, the dimensions of a rectangle are 8 and 12 feet and they are inreasing at the…

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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 stone dropped in a pond sends out a circular ripple whose radius increases at a constant rate of 2…

A: Given ,  A stone dropped in a pond sends out a circular ripple whose radius increases at a constant…

Q: A balloon leaving the ground 60 ft. from an observer, rises vertically at the rate of 10 ft. per…

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Q: . A 6-ft tall man is walking away from a 15-ft tall street lamp at the rate of 5 ft/sec. How fast is…

A:

Q: The radius of a sphere is increasing at a rate of 4 meters per minute. When the radius is 11 meters,…

A:

Q: as a balloon in the shape of a sphere is being blown up, the volume is increasing at the rate of 4…

A: Volume of the sphere Shape ballon: V = 4/3ℼr3   (r = radius)   Now differentiate with respect to L,…

Q: . A vertical cylinder is leaking water at a rate of 1 ft /sec. If the cylinder has a height of 10 ft…

A:

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

A:

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.…

A:

Q: When a metal plate is heated, it expands. If the shape of the plate is circular and its radius is…

A: When a metal plate is heated, it expands. If the shape of the plate is circular and its radius is…

Q: The base x of the right triangle in the figure increases at a rate of 6 cm/s, while the height remai

A: In this question we will use basic of calculus i.e application of differentiation. We will first…

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…

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

A:

Q: A 15-foot ladder is slider down a wall at a rate of 3 ft/sec.  At what rate is the bottom of the…

A:

Q: 5 If a snowball melts so that its surface area decreases at a rate of 10 cm2/min, find the rate at…

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