When calculating the volume of a solid when revolving on either axis, if a particular axis is not given within the question, how does one figure on which axis the function is revolving around?

Q: A certain bacterial cell is spherical in shape. What is the approximate increase in the volume of…

A: given initial radius r= 2.2 mm after increasing , radius = 2.3 mm change in radius ∆r = 2.3-2.2 =…

Q: 1. Given: y 3x Assuming the box has a fixed volume. What is the value of y in terms of x that will…

A: First find the volume then differentiate on both side .

Q: An oil storage tank can be described as the volume generated by revolving the area bounded by y = x…

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Q: The base of a three-dimensional figure is bound by the line y = √x + 2 on the interval [-1, 1].…

A: We have to find the volume of bounded region in the interval [-1,1].

Q: An open box with a square base is to have a volume of 18 ft3 Find the box dimensions that minimize…

A: Consider the thickness of the material to be negligible.Since the base is square shaped, the length…

Q: What is the exact volume of the solid stretching over the x-interval [0, 2] whose cross-sections are…

A: Given query is to find volume of the solid generated.

Q: An icicle is gradually increasing in length, whilemaintaining a cone shape with a length 15 times…

A: It is given that an icicle is gradually increasing in length, while maintaining a cone shape with a…

Q: A one compartment vertical file is to be constructed by bending the long side of an 8 in. by 16 in.…

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Q: A conical vessel has a height of 24 cm and a base diameter of 12cm. It holds water to a depth of 18…

A: Draw a schematic diagram of given question.

Q: The radiusof an air bubble is increasing at the rate of 0.5cm/ sec At what rate if the volume of the…

A: Rate of change

Q: ) About how accurately must the interior diameter of a cylindrical storage tank that is 8 m high be…

A: Given: Internal diameter of tank = d

Q: Derive the general formula for volume of x = x^3 , x-axis, x = 8 by circular disk method

A: Obtain the general formula for volume of y = x3, x-axis, x = 8 by circular disk method as follows.…

Q: Approximate the change in the volume of a right circular cylinder of fixed radius r= 19 cm when its…

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Q: What is the exact volume of a solid that is formed by rotating the function h (x) = 4/x about the…

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Q: An open box is to be made from a 6 ft by 16 ft rectangular cardboard by cutting out equal squares…

A: Find the maximum volume  by derivative

Q: The base of a three-dimensional figure is bound by the line y = x² on the interval [0, 2]. Vertical…

A: Formula: If the area of the cross-sections of a solid at x is Ax for a≤x≤b, then the volume of the…

Q: Water is leaking out of an inverted conical tank at a rate of 7500 cubic centimeters per min at the…

A: In this we have to follow some basic concepts so for better understanding I'm providing hand written…

Q: Use the cylindrical shell method to calculate the exact volume of the solid formed by rotating the…

A: Given problem:- Use the cylindrical shell method to calculate the exact volume of the solid formed…

Q: A solid is 3 m high. The cross-section of the solid at height x meters above its base has area 2z…

A: Volume is equal to base area multiolied by height.

Q: A spherical snowball is melting in such a way that its radius is decreasing at a rate of 0.2 cm/min.…

A: Given that a spherical snowball is melting in such a way that its radius is decreasing at a rate of…

Q: How can I derive the formula for volume (of any shape) and how can it be used?

A: Volume:- It is defined as the three-dimensional space enclosed by a boundary or occupied by an…

Q: A mineral deposit along a strip of length 6 cm has density s(x) = 0.01x(6 − x) g/cm for 0 ≤ x ≤ 6.…

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Q: 4. A water trough is 8 m long, and a cross section has the shape of an isosceles triangle that is…

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Q: 5. A spherical balloon is inflated so that its volume is increasing at the rate of 2 m'/min. At what…

A: Let r be the radius of the balloon and D be the diameter.

Q: 4. Using differential, determine the error in computing the volume of a cube if the error in…

A: Error in volume

Q: An atom of a particular element has a volume of 7.8x10^-31 m^3. What is the volume in cubic…

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Q: The radius of a right circular cone is increasing at a rate of 1.5 in/s while its height is…

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Q: Find the volume of the solid whose base is a circle of radius one, and cross sections perpendicular…

A: Given:   Find the volume of the solid whose base is a circle of radius one, and cross sections…

Q: A village wishes to measure the quantity of water that is piped to a factory during a typical…

A: Given :         A gauge on the water line gives the flow rate (in cubic meters per hour) at any…

Q: is full of water. Calculate the work required to pump the water through an opening at the top of the…

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

Q: What is the exact volume of a solid that is formed by rotating the function h (x) = 6/x about the…

A: Explained below...

Q: A certain pine tree maintains the shape of a cone. When the base of the tree is 28 ft in diameter,…

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Q: Use the cylindrical shell method to calculate the exact volume of the solid formed by rotating the…

A: Using shell method volume is estimated.

Q: 2) A box with height h has a square base with length x. The error in measuring the side of the base…

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Q: A certain solid is 1 ft high, and a horizontal cross section taken x ft above the bottom of the…

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Q: ) Use the cylindrical shell method to calculate the exact volume of the solid formed by rotating the…

A: I am going to solve the given problem by using some simple geometry to get the required result of…

Q: An inverted conical tank has a top radius of 2m and a height of 8m and is completely filled with…

A: Given Inverted conical tank of radius 2cm height 8cm    Solution Volume of initially water…

Q: Given the area  in the first quadrant by x^2 = 8y, the line x = 4 and the x axis. What is the volume…

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Q: ie the total surfoce area of a Cylinder lfloor,ceiling an d lateral area to tal) is 300m unit…

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Q: A thin metal plate is shaped like a semicircle of radius 4 in the right half-plane, centered at the…

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Q: What are the dimensions of a closed rectangular box that has a square cross section, a capacity of…

A: Here we want to find the dimensions of the given rectangular box having volume of 101 in³ it is…

Q: Calculate the volume of the rotating object that occurs if the area in the first quadrant is bounded…

A: Calculate the volume of the rotating object that occurs if the area in the first quadrant is bounded…

Q: What is the exact volume of the solid stretching over the X-interval [0, 2] whose cros-sections are…

A: Volume of solid is 20.49

Q: A quantity of gas with an initial volume of 1 cubic foot and a pressure of 500 pounds per square…

A:

Q: A thick rope of length 30 meters is hanging over the edge of a tall building. During the night, it…

A: Given: A thick rope of length 30 meters is hanging over the edge of a tall building. During the…

Q: A colony of bees lives in an ever-growing beehive that is in the shape of a sphere. Use The volume…

A: 20 new bees are added to the hive each week. Each bee in the colony needs 5 cm3 of space. (space…

Q: A spherical snowball is melting in such a way that its radius is decreasing at a rate of 0.4 cm/min.…

A: Given: Spherical snowball is melting in such a way that its radius is decreasing at a rate of 0.4…

Q: A tank, with a rectangular base measuring 10 cm ☓ 20 cm is 1/3 filled with water to a depth of 18…

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Q: What is the exact volume of a solid that is formed by rotating the function g(x) = 3x2 + 4 about the…

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Q: A certain gas expands to fill a 3 L container. Its mass is measured to be 0.6 kg. What is its…

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