Throwing a stone in a small lake results in circular ripples. When the circle has radius 10 ft, the radius in increasing at a rate of 2 ft / min. Find the rate at which the area of the cicular ripple is increasing at this moment.

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: The radius of a sphere increases at a rate of 4m/sec. Find the rate at which the surface area…

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Q: A Ferris wheel with a radius of 15 m is rotating at a rate of one revolution every two minutes.…

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Q: A water tank has the shape of an inverted circular cone with base radius 2m and height 4m. If water…

A: The volume of the tank is a circular cone, therefore it is given by:                          V =…

Q: The radius of a sphere increases at a rate of 4m/sec. Find the rate at which the surface area…

A: Rate at which surface area increases is

Q: An oil slick on a lake is surrounded by a floating circular containment boom. As the boom is pulled…

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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: The area of a circle increases at a rate of 4 cm? /s. a. How fast is the radius changing when the…

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

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Q: The side of a cube decreases at a rate of 8 m/sec. Find the rate at which the volume changes, when…

A: given that a side of cubedecreases at a rate of 8m/sfind the rate at which the volume changes when…

Q: If a snowball melts so that its surface area decreases at a rate of 7 cm2/min, find the rate at…

A: Solve using increasing & decreasing function.

Q: If a snowball melts so that its surface area decreases at a rate of 9 cm2/min, find the rate at…

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

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Q: Vater is being poured at the rate of 2x m' /min into an invertedi with a radius of 6 meters at the…

A: Let the radius of the inverted conical tank =r=6 m Height of the conical tank =h= 12 m Pouring rate…

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

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Q: If a snowball melts so that its surface area decreases at a rate of 9 cm2/min, find the rate at…

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Q: How fast is the bicycle traveling in miles per​ hour? (Hint: 5280 ft=1 mi)

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Q: An oil tanker aground on a reef is forming a circular oil slick about 0.1 foot thick. If the oil was…

A: Given that  An oil tanker aground on a reef is forming a circular oil slick about 0.1 foot thick. If…

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: The side of a cube decreases at a rate of 7 m/sec. Find the rate at which the volume changes, when…

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Q: A cylindrical box has a fixed height of 12 inches. Find the rate of change of volume with respect to…

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Q: a water tank has the shape of an inverted circular cone with a base radius of 2m and a height of 4m.…

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Q: Water flows into a conical tank at a rate of 2 ft3>min. If the radius of the top of the tank is 4…

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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…

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Q: Sand is leaking through a small hole at the bottom of a conical funnel at the rate of 12rcm³ / s. If…

A: Given: Radius of the funnel r=8 cm. Height of the funnel h= 16 cm. rate of change of volume…

Q: The radius of a circle increases at a rate of 4 cm/ sec. The rate at which the area of the circle…

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Q: A boy is blowing a spherical balloon at a rate of 50cm3/s. At what rate is the radius of the balloon…

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Q: The radius of a sphere decreases at a rate of 8 m/sec. Find the rate at which the surface area…

A: It is given that the radius of sphere decreases at a rate of 8 m/sec. So, drdt=-8. The radius is r=3…

Q: A Helium is being pumped into a spherical balloon at a rate of 12cm³/min. Determine the rate at…

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Q: A spherical party balloon is being inflated with helium pumped in a rate of 7 cubic feet per minute.…

A: Given,           A spherical party balloon is being inflated with helium pumped in a rate of 7 cubic…

Q: The radius of a sphere increases at a rate of 3m/sec. Find the rate at which the surface area…

A: The surface area is

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

A: Given

Q: If a snowball melts so that its surface area decreases at a rate of 4 cm4/min, find the rate at…

A: Note that snowball has a shape of sphere.

Q: The radius of a sphere increases at a rate of 3m/sec. Find the rate at which the surface area…

A: Rate of change of radius = 3m/s Find the change in surface area at radius = 6m

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

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

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Q: Sand is leaking through a small hole at the bottom of a conical funnel at the rate of 12rcm³ /s. If…

A: Given-  dVdt=12π cm3sec.,R=8 cm and H=16 cm To find- depth of sand after 15seconds and the rate of…

Q: If a snowball melts so that its surface area decreases at a rate of lcm²/min, find the rate at which…

A: Snowball represents a sphere So , Surface Area of sphere is 4πr2.  And , d=2r.  Using this we solve…

Q: pouring

A: We will find the rate of change of height.

Q: A spherical balloon is being inflated at the rate of 12m /min. If the radius of the balloon is 6m,…

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Q: A man walks along a straight path of 4m/s. A searchlight is located on the ground 25m from the path…

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Q: A Ferris wheel with a radius of 5 m is rotating at a rate of one revolution every 2 minutes. How…

A: Explained below

Q: The radius of a circle is increasing at a rate of 3 ft/min. At what rate is its area changing when…

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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…

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