2. The radius of a cylinder is increasing at a rate of 1 meter per hour, and the height of the cylinder is decreasing at a rate of 4 meters per hour. At a certain instant, the base radius is 5 meters and the height is 8 meters. What is the rate of change of the volume of the cylinder at the instant?

Q: 7. A triangle with a base of 20 inches has a height that is decreasing at a rate of 3 inches per…

A:

Q: 4. A baseball diamond is a square 90 ft on a side. A player runs from first base to second base at…

A:

Q: 3. The radius of a spherical balloon is increasing at the rate of 2 cm per minute. How fast is the…

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Q: 11. If the base of a triangle is constantly 4 cm, find the rate at which the area of the triangle is…

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: A balloon leaves the ground 18m from an observer and rises vertically at 1.25 m/s. How fast is the…

A: "Since you have asked multiple questions,we will solve first question for you. If you want any any…

Q: 2)The radius of a sphere decreases at the rate of 1 m/sec. Find the rate at which the volume…

A: Given,  The radius of a sphere decreases at the rate of 1 m/sec  We have to find the rate at which…

Q: 12. The height of a right circular cone is increasing at 3mm/s and its radius is decreasing at…

A: Volume of a right circular cylinder is given by formula,  V=πr2h , where r is the radius of circular…

Q: 16.Suppose that the dimensions of a cylinder change at constant rates: the radius of the base is…

A: Use the derivative and substitute the given values.

Q: Suppose a snowball remains spherical while it melts, with the radius r shrinking at 4 inch(es) per…

A: Let r be the radius of the snowball at any time t. The radius r is decreasing at the rate of 4 in/hr…

Q: 13. A plane flying horizontally at an altitude of 1 mi and a speed of 500 mi/h passes directly over…

A:

Q: 2. A fighter plane 2,000 km away is spotted by a gunner in the ground. If it maintains its altitude…

A:

Q: The radius of a cylinder is increasing at a rate of 1 meter per hour, and the height of the cylinder…

A:

Q: 8. The radius of an inflating balloon in the shape of a sphere is changing at a rate of 3cm/sec. At…

A:

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

A:

Q: Suppose that liquid is to be cleared of sediment by allowing it to drain through a conical filter…

A: Solution: Consider the given conical filter with height h = 16 cm and radius r = 4 cm we have V =…

Q: A cubic block of ice whose side is 2 inches long is melting at a rate of 1 in^3 per minute. How fast…

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: 3 The altitude of a triangle is increasing at a rate of 8 cm/s while its area is increasing at the…

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: 2. The radius of a sphere decreases at the rate of 5 m/sec. Find the rate at which the volume…

A: Given that the Radius of sphere decreases at the rate of 5m/sec and radius is 5 m

Q: The sides of a square increase in length at a rate of 4 m/sec. a. At what rate is the area of the…

A: Area of square = a2 Where a is length of side of square.

Q: 1. A spherical balloon is being inflated so that the volume is increasing at the rate of 5 ft.³ per…

A:

Q: 16. If the radius of a circle is increasing at the rate of 4 cm/s, find the rate of the increase in…

A: Given radius of a circle is increasing at the rate of 4 cm/sec.

Q: A liquid solution is passing thru a conical filter 2 feet deep and 4/3 feet across the top, into a…

A: We have to find the rate at which the level of the solution in the cylinder rising.

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

A: Please refer the attached image for complete solution.

Q: 2)The radius of a sphere decreases at the rate of 4 m/sec. Find the rate at which the volume…

A: We need to find the rate at which volume decrease when radius is 3m

Q: 3. The radius of a cylinder is increasing at a rate of 4cm/sec. The surface area remains constant at…

A: Given

Q: A cylinder is leaking water but you are unable to determine at what rate. The cylinder has a height…

A: Given, Radius is 2m, height is 2m. Height is decreasing at 10 cm/min when height is 1m.

Q: 20. The length of a rectangle is increasing at a rate of 5 cm/sec and the width is decreasing at a…

A:

Q: 7. The radius of a cylinder is increasing at a rate of 1 meter per hour, and the height of the…

A: let r be the radius of cylinder    h be the height of cylindergiven drdt = 1 mhrdhdt = -4 mhrwhen r…

Q: 15) The volume of a sphere is increasing at a rate of 6 cm³/sec. Find the rate of change of its 4T…

A:

Q: 6. The radius of a right circular cylinder is increasing at the rate of 3in/sec, while the height is…

A:

Q: The radius of a cylindrical tube is increasing at a rate of 2 meters per hour, and the height of the…

A: Cylinder is a figure with circular base with a certain height. We can see it as the below diagram.…

Q: Suppose that liquid is to be cleared of sediment by allowing it to drain through a conical filter…

A: Given,

Q: 2. The radius of a sphere is decreasing slowly at the rate of 2 cm/week. How fast is the volume…

A: Consider the given information. The volume of the sphere is defined as, V=43πr3

Q: 9. The altitude of a triangle is increasing at a rate of 2 cm/min while the area of the triangle is…

A: Area of triangle = 12×b×h Where b is base and h is height . And height of the triangle is equal to…

Q: 1. A spherical balloon is expanding. If the radius is increasing at the rate of 2 inches per minute,…

A: The given question can be solved as shown in step2.

Q: 2)The radius of a sphere decreases at the rate of 1 m/sec. Find the rate at which the volume…

A:

Q: Suppose the area A of a particular rectangle increases at a rate of 2 cm^2/sec and the width w of…

A:

Q: 5. Two parallel sides of a rectangle are being lengthened at the rate of 20 mm/sec, while the other…

A: Given that the lengths of the rectangle are begin increased at the rate of 20 mm /sec. The other two…

Q: 16. A plane flying horizontally at an altitude of 1 mi and a speed of 500 mi/h passes directly over…

A:

Q: 4. Water is running out of a conical tank 3 m across the top and 4 m deep at the rate of 2 m3 /min.…

A: given  h = 4 m  (Note: measurement of h is always taken from bottom) r = (3 ÷ 2 ) = 1.5 m dVdt = 2…

Q: Water is poured into an inverted conical cistern of altitude 12 ft and radius of base 5 ft. If the…

A: Use the following formulae, to obtain the solution.  Volume of the Cone=13πr2h Where r and h is the…

Q: Find the rate of bubble volume increasing when the radus is 4cm if its surface area is increasing at…

A: Given: dSdt=4  cm/secdVdt|r=4 cm=?

Q: 2) The radius of a sphere decreases at the rate of 4 m/sec. Find the rate at which the volume…

A:

Q: 2. The height and volume of a right circular cone change at the rates of 1 cm/s and -2 cm^3/s,…

A: Let's find.

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: 5. The area of an equilateral triangle is decreasing at a rate of 4 sq. cm. per minute. Find the…

A: