If the volume of a different sphere is increasing at a rate of 24 cubic inches per minutes and the surface area is increasing at the rate of 12 square inches per minute, what is the radius of the sphere?

Q: The volume of an ice cube is decreasing at a rate of 1.5 cm³/ sec. At what rate is a side of the ice…

A: We know that volume of a cube is given by V=a3 here V=volume of cube ,a=edge of cube Rate of change…

Q: The radius of a sphere decreases at a rate of 1 m/se decreases when the radius is 15 m

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Q: Two cars start moving from the same point. One travels south at 48 mi/h and the other travels west…

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Q: The volume of a cube is increasing at a rate of 64 in/sec. At what rate is the length of each edge…

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

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Q: The lengths of the edges of a cube are increasing at a rate of 1 ft/min. At what rate is the surface…

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Q: A spherical drop of liquid evaporates at a rate proportional to its surface area. If a given drop…

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Q: The volume of an ice cube is decreasing at a rate of 1.5 cm³/sec. At what rate is a side of the ice…

A: option A is correct detailed solution with explanations given below

Q: The volume of a cube is increasing at a rate of 60 in/sec. At what rate is the length of each edge…

A: The objective is to find the rate at which the length of each edge of the cube is changing when the…

Q: The pressure exerted by a certain liquid at a given point varies directly as the depth of the point…

A: Given            The pressure at 70 feet=140

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: If the diagonal of a cube is increasing at a rate of 3 cubic inches per minute, how fast (in…

A: We will find the rate of increase of side of cube.

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

A:

Q: Each side of a square is increasing at a rate of 5 cm/s. At what rate is the area of the square…

A: Let,

Q: The width of a rectangle is increasing at a rate of 5 cm/sec, while the length increases at 6…

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

A:

Q: If the rate of change in volume of a sphere is equal to its rate of change of its radius. What is…

A: if we let the radius of square = r unit then volume of the square =4/3 πr3 unit3

Q: The height of a right circular cylinder is 50 inches and decreases at the rate of 4 inches per…

A: Topic = Volume

Q: An airplane flying on a straight flight path will be exactly above a radar tracking station, which…

A: Given: Perpendicular distance between station and plane is 5,000 km To find rate of distance of…

Q: All edges of a cube are expanding at a rate of 8 mm per hour. At what rate is the volume of the cube…

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Q: If the volume of a cube is increasing at a rate of 24 in'/min and each edge is increasing at 2…

A: The volume of cube is given by V=a3 where a edge of cube. Given that volume of cube increasing at a…

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

A: Each side of a square is increasing at a rate of 6 cm/s. To determine the rate at which the area of…

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: If the ocean is opening at a rate of 3 cm/year., how wide will the ocean be in 100 million years in…

A: If the ocean is opening at a rate of 3 cm/year, then we have to find how much wide will the ocean be…

Q: If the radius of a sphere is increasing at the constant rate of 3 inches per second, how fast is the…

A: Given dr/dt = 3

Q: When the lid is left off an ink bottle, the ink evaporates at a rate of 2.5 x 20 "cm" bottle…

A: Given that: Rate at which ink evaporates=2.5×10-6cm3s and Total volume of ink in the bottle is 36…

Q: Each side of a square is increasing at a rate of 3 cm/s. At what rate is the area of the square…

A: Let the length of side of square be' a '

Q: A baseball diamond has the shape of a square with sides 90 ft long, as shown. A player is running…

A: A baseball diamond has the shape of a square with sides 90 feet long. A player running from second…

Q: The length of the horizontal leg of a right triangle is increasing at a rate of 3 ft/sec, and the…

A: Given A right triangle  horizontal leg = 7ft vertical leg = 1ft

Q: Two cars start moving from the same point. One travels south at 64 mi/h and the other travels west…

A:

Q: The volume of a cube is increasing at a rate of 68 in3/sec. At what rate is the length of each edge…

A: Related rates of changes –                 The related rate of change is finding the rate of change…

Q: The volume of a cube is increasing at the rate of 1200 cm3/min at the instant its edges are 20 cm…

A: Let the length of the sides of the cube = xAnd the volume of the cube = V = x^3

Q: A cylindrical pool has a height of 8 feet and radius of 6 feet. How fast is the volume (in cubic…

A: Volume of cylindrical shape V=πr2h ------------------(1)

Q: he surface area of a cube is increasing at a rate of 122.2 cm2/s. At what rate is the side length of…

A:

Q: If the area of a square is increasing by 10 square inches per minute, how quickly is the length of…

A: Let us consider x inches be the side of the square. Area = x2. We are given that the area of the…

Q: The volume of a cube is increasing at the rate of 1200 cm³ / min at the instant its edges are 20 cm…

A:

Q: an ice cube is shrinking uniformly at a rate of 8 cubic inches per hour. when the cube has a volume…

A: We are given the rate of change of volume of ice cube is shrinking uniformly at a rate of 8 cubic…

Q: A conical tank 20 feet in diameter and 30 feet tall (with vertex down) leaks water at a rate of 5…

A: To find the rate of water

Q: The volume of a cube is increasing at a rate of 64 in ³/sec. At what rate is the length of each edge…

A:

Q: How long (in hours) would it take to fill a city water tank that has an inside diameter of 120 feet…

A:

Q: The pressure exerted by a certain liquid at a given point varies directly as the depth of the point…

A:

Q: The length of a rectangle is increasing at a rate of 2 ft/s, and its width is increasing at a rate…

A: Here we have, The length of a rectangle is increasing at a rate of 2 ft/s, and its width is…

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

A:

Q: Each side of a square is increasing at a rate of 7 cm/s. At what rate is the area of the square…

A: If the area of a square, A, is x2 units , then the length of its side is x unit .

Q: The volume of a cube is increasing at a rate of 56 in/sec. At what rate is the length of each edge…

A: Given that the volume of a cube is increasing at a rate 56 in3/sec and the edges are 8 in. long. It…

Q: The pressure exerted by a certain liquid at a given point varies directly as the depth of the point…

A:

Q: If the area of a circle decreases constantly by half a square foot per second, at what rate is its…

A: Here, given that the area of the circle decreases constantly by half s square foot per second. That…

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

A: Suppose that the length of rectangle is “l” and width is “w”   So according to the question, dwdt=2…