The radius of a spherical ball is increasing at a rate of 2 cm/min. At exactly what rate (in cm²/min) is the surface area of the ball increasing when the radius is 6 cm? cm?/min

Q: All edges of a cube are expanding at a rate of 8 centimeters per second. (a) How fast is the surface…

A: Surface area of cube = 6x2Where x is the edge of the cube

Q: 4. A stone dropped in a pond sends out a circular ripple whose radius increases at a constant rate…

A:

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

A: At a certain instant the dimensions of a rectangle are: Length L=8 feetWidth W=12 feet

Q: The radius of a sphere is increasing at a rate of 2 mm/s. How fast is the volume increasing when the…

A: Write the expression for the volume of the sphere and take the derivative then substitute the given…

Q: Suppose that a shallow earthquake occurs in which the P waves travel 8 km/sec and the S waves travel…

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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: 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: A cylindrical column is (3m) high and (0.2m) radius, if the radius of the column increases at a rate…

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

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: 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 length of a rectangle is increasing at a rate of 3 cm/s and its width is increasing at a rate of…

A:

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: If a snowball melts so that its surface area decreases at a rate of 3 cm/min, find the rate (in…

A: Given  Decreasing rate of surface area = 3cm2/min To find: the rate of decreasing of diameter when…

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

A: Rate of increase of radius of a spherical ball,drdt= 2 cm/min Radius of the ball = 9 cm

Q: A spherical balloon is inflated so that its volume is increasing at the rate of 2.2 ft^3/min. How…

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Q: The volume of a cylinder with a radius of 5 inches is increasing at a rate of 36pi in^3/min. How…

A: given in a cylinderr=5 indVdt=36π in3/minh=10 innow volume of cylinder (V)=πr2hradius is constant

Q: All edges of a cube are expanding at a rate of 3 centimeters per second. (a) How fast is the volume…

A:

Q: The length of a rectangle is increasing at a rate of 3 cm/s and its width is increasing at a rate of…

A: Consider the given situation, Let the length of the rectangle be ‘l’ and breadth be ‘b’.Area of…

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 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 pebble is dropped into a calm pond, causing ripples in the form of concentric circles, as shown.…

A:

Q: A spherical balloon is inflated so that its volume is increasing at the rate of 2.8 ft^3/min. How…

A: Given  dVdt=2.8  ft3/ min and D=1.6 ft

Q: The radius r of a sphere is increasing at a rate of 4 inches per minute.

A:

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: The edge length of a cube is 12 cm and increasing at a rate of 2 m. How fast is the Surface Area of…

A: Given dx/dt=2cm/hr X=12cm

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 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 drop of liquid evaporates at a rate proportional to tis surface area. If a given drop…

A: Given: The drop evaporates to 18 of its volume in 5 minutes

Q: If the base h of a triangle is increasing at a rate of 3 inches per minute while its height h is…

A: Area of a triangle of base b and height h is given as, A=12bh The derivative of area with respect to…

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

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Q: 1. How fast is the water level rising in a rectangular fish tank whose base is 20 ft² if the tank is…

A: Give: Area of base is A=20 ft2 Rate with which tank is filling dVdt=0.5 ft3/min. Volume of a…

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

A: Given ,The radius of a sphere , initially zero , increases at the rate of 6 per second.The volume is…

Q: Each side of a square is increasing at a rate of 2 cm/s. At what rate (in cm2/s) is the area of the…

A:

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

A: Given Volume of cube increasing at a rate of 68 in3/ secTo the rate of change of length of each edge…

Q: a kite 100 ft ft above the ground moves horizontally at a speed of14ft/s. at what rate is the…

A: If you like the solution then please give it a thumbs up..... The Answer is:     Result = - 0.035…

Q: The original 24 m edge length x of a cube decreases at the rate of 4 m/min. a. What rate does the…

A: Here, We need to find a) The rate at which cube's surface area change when x=5 m b) The rate at…

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: Each side of a square is increasing at a rate of 3 cm / s . At what rate (in cm^ 2 /s) is the area…

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 area of a rectangle is increasing at a rate of 4 cm/sec ? while the width of the rectangle…

A: The area of a rectangle is increasing at a rate of 4 cm/sec ? while the width of the rectangle…

Q: 1. The width of a rectangle is increasing at a rate of 2 cm/sec, while the length increases at 3…

A: I have stated the used formulas in the solution

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

A:

Q: The length of a rectangle is increasing at a rate of 5 cm/s and its width is increasing at a rate of…

A: We have to find