The radius of a spherical balloon is decreasing at a rate of 2 - in/sec. Which of the following is the rate of change of volume (in cubic inches/second) when the radius of the balloon is 4 inches?

Q: A spherical balloon is inflated and its volume increases at a rate of 30 in3 /min. (a). What is the…

A: Given that, The spherical balloon is inflated and its rate of change of volume is; dVdt=30 (in3min)…

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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…

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Q: The volume of a sphere is increasing at a rate of 4 cm3/sec. Find the rate of change of its surface…

A: We will use derivative as rate of change

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Q: A hot-air balloon is 140 ft above the ground when a motorcycle (traveling in a straight line on a…

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A: Let x be the horizontal distance from balloon to motorcycle, y be the vertical distance from the…

Q: The radius of a sphere is increasing at a rate of 4mm/s. How fast is the volume increasing when the…

A: The rate of change of the radius of the sphere, drdt = 4 mm/s To evaluate : The rate at which the…

Q: The volume of a metal in a hollow spherical is constant. If the inner radius is increasing at thr…

A:

Q: The radius of a circle is increasing at the rate of 4 cm/s. How fast is the area of the circle…

A: Given,           The radius of a circle is increasing at the rate of 4 cm/s. And the radius is 5 cm…

Q: An inverted conical tank with a height of 6 feet and a diameter of 4 feet that was filled with water…

A: It is given that, the height and diameter of the conical tank is 6 feet and 4 feet, respectively.Let…

Q: The radius of a spherical balloon is increasing at the rate of 2 cm per minute. How fast is the…

A: Let r be the radius of spherical ballon

Q: A spherical balloon is deflating at a rate of 0.57 in /sec. How fast is the radius changing, in…

A: Let  The radius of the sphere is r. Volume of the sphere is  V=43πr3 Differentiate the volume with…

Q: The radius of a circle is increasing at the rate of 0.7 cm/s. what is the rate of

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Q: A spherical balloon is expanding. If the radius is increasing at the rate of 2 inches per minute, t…

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Q: The area A of a circle is increasing at a constant rate of 2cm's-. If the area of the circle is…

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Q: Water is discharged from an inverted cone-shaped tank with a height of 12 meters and a radius of 6…

A: Given: The height of the inverted cone-shaped tank, h = 12m. Also, its radius, r = 6m. From the…

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: A perfectly spherical balloon is losing volume at a rate of 3 in3 per sec. How fast is the balloon’s…

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Q: A balloon has just been inflated. Calculate the instantaneous rate of change by which the area…

A: Introduction: A geometric shape with a sphere-like appearance. In three dimensions, the sphere is…

Q: The height h of a right circular cylinder is twice its radius r. Find the rate of the volume V of…

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Q: The hour hand of a clock is 4 inches long and the minute hand is 6 inches long. At the moment the…

A: The hour hand of clock is 4 inches long and the minute hand is 6 inches long. At that time angle…

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Q: The surface area of a sphere, initially zero, increases uniformly at 4 square inches pe second. Find…

A: Since you have asked multiple questions here, we will solve the first question for you. To get the…

Q: The area of a circle increases at a rate of 4 cm2 / s. a. How fast is the radius changing when the…

A: I have given an answer in step 2.

Q: The radius r of a sphere is increasing at a rate of 8 inches per minute. Find the rate of change of…

A: We know that volume of a sphere is given byV= 43πr3 where r be the radius of the sphere.Now we are…

Q: The radius of a right circular cone is increasing at 3 cm/min whereas the height of the cone is…

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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: As an orange grows, the rate of change of the radius r of the orange is inversely proportional to…

A: Given query is to find differential equation.

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: The radius of a right circular cylinder is increasing at the rate of 8 in/sec while the height is…

A: Given- drdt=8 in/sec and dhdt=-3 in/sec To Find- The rate of the volume changing when r= 7 in and…

Q: The radius of semicircle is increasing at the rate of 0.8 cm/s, calculate the rate of change in the…

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Q: A kite, at a height of 60ft.is moving horizontally at rate of 5ft./sec away from the boy who flies…

A: In right angle triangle ,According to the Pythagoras theorem , H2 = P2 + B2 Where H is horizontal ,…

Q: A spherical balloon is deflated at a rate of 10 cm3 s-1. Find the rate change of the surface area…

A: given: A spherical balloon is deflated at a rate of 10 cm3s-1. we have to find the rate change of…

Q: The side of a square is increasing at the rate of 0.2 cm/sec . Find the rate of increase of the…

A: we know that the perimeter of the square is with side x is                        P=4x…

Q: Air is being pumped into a spherical balloon such that its radius increases at a rate of .50 in/min.…

A: r= 3 in dr = 0.5 in/min

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

A: Given,            A balloon leaving the ground 60 ft from an observer rises vertically at the rate…

Q: A hot air balloon is 120 ft. above the ground when a motorcycle (travleing in a straight line on a…

A: Given that, A hot air balloon is 120 ft. above the ground when a motorcycle (traveling in a straight…

Q: A weather balloon is rising vertically at the rate of 10ft/s. An observer is standing on the ground…

A: Given: -

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Q: The surface area of a cube with sides of length x is given by S = 6x2 . Find the rate of change of…

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Q: The volume of a sphere is increasing at a rate of 8 cm3/sec. Find the rate of change of the radius…

A: Given : V= 32π/3 cm3              dV/dt = 8 cm3 /sec

Q: The diameter of a sphere is 5(2x+ 5), the rate of change of its surface area with respect to x is

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