The radius of the base of a cylinder is increasing at a rate of 1 m/h and the height of the cylinder is decreasing at a rate of 4 m/h. A certain instead, the base radius is 5 m and the height is 8 m. What is the rate of change of the volume of the cylinder at that instant

Q: 2. Sand is being dropped at the rate of 10ft.3/min into a conical pile. If the height of the pile is…

A:

Q: The length of a rectange is increasing at a rate of 8 cm/s and its width is increasing at a rate of…

A:

Q: The length of the rectangle is increasing at a rate of 5 cm per second, and its width is decreasing…

A: topic - application of derivatives

Q: A conical shaped heap of sand is growing (picture sand being added from above at its peak). If the…

A:

Q: The radius of a right circular cone is increasing at a rate of 1.1 in/s while its height is…

A: Given that, drdt=1.1 in/s and dhdt=-2.7 in/s. Also, it is given that r=102 in. and h=162 in. It is…

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 rectangular box has its height increasing at a rate of 1m/s while its volume is decreasing at a…

A: We have to find the  rate of change of length.

Q: The length of the rectangle is increasing at a rate of 5 cm per second, and its width is decreasing…

A: Area of rectangle = Length * Width

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

A:

Q: A ladder of length 3 meters is placed on a wall, with the distance from the wall x and the height of…

A:

Q: The edge of an expanding cube is changing at the rate of 2.3 cm/s at the instant its edge is 18.3 cm…

A:

Q: A sperical snowball is melting in such a way that its volume is decreasing at a rate of 1 cm^3/min.…

A: Volume of the sphere formula:‘r’ is the radius of the sphere

Q: An inverted conical water tank with a height of 12ft and a radius of 6ft ft is drained through a…

A:

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

A: Let the sides of rectangle be x and y   since, two parallel sides are increasing at the rate of…

Q: A man of 2 mts tall is approaching a lamp post at the rate of 0.5m/sec.if the lamp post is situated…

A:

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: A balloon, in the shape of a right circular cylinder, is being inflated in such a way that the…

A:

Q: An 8- meter ladder is leaning against a vertical wall. If a the ladder away from the person pulls…

A: Given  Length of the ladder = 8 meter The rate at which ladder is pulled away from the wall =0.7m/s…

Q: 1. If the radius of a spherical balloon is increasing at the rate of 3 cm/s, which of the following…

A: We are only allowed to solve one question at a time so we will answer only the first question.…

Q: If a snowball melts so that its surface area decreases at a rate of 3 cm2/min, find the rate at…

A: As per our guidelines, we can answer only one question in a single request. Kindly re-post the other…

Q: The radius of a right circular cone is increasing at a rate of 1.2 in/s while its height is…

A: To calculate the required rate of change using partial derivatives

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

A:

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

A: The volume of the right circular cylinder is given as: V=πr2h where 'r' is the radius of the cone…

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…

Q: 2) A person is standing 350 feet away from a model rocket that is fired straight up into the air at…

A:

Q: Suppose that water is pouring into a swimming pool in the shape of a right circular cylinder at a…

A: Given that radius =7 ft dVdt=9 cubic ft per minutefind dhdt Also V=πr2h

Q: The side of the base of a square prism is decreasing at a rate of 7 km/min and the height of the…

A: Surface area of a square prism is given by- A=2a2+4ah where a is side of prism, h is height of…

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

A:

Q: A weather balloon is rising vertically at the rate of 2 m/sec. An observer is standing on the ground…

A: The diagram of the given question will be as follows Given: dydt=2 m/s To find: dxdt

Q: The length of a rectangle is increasing at a rate of 8 cm/s and its width is increasing at a rate of…

A:

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

A: given that plane is flying horizontally at an altitude of 1mi speed=500 mi/h find the rate at which…

Q: A box has a length increasing at a rate of 2 in/s, a height decreasing at a rate of 3 in/s, and a…

A:

Q: The radius of a right circular cone is increasing at a rate of 5 in/s while its height is decreasing…

A: Let,  r - radius of the right circular cone h-Height of the right circular cone  V- Volume of the…

Q: Two parallel sides of a rectangle are lengthened at a rate of 3 cm/sec, while the other sides are…

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: 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: If the radius of a sphere increases at a rate of 0.5 m/sec, then the rate at which the volume of the…

A: Let the radius of the sphere be r. Then the volume of the sphere is: V=43πr3…

Q: An inverted conical tank 10 m high and 3 m radius at the top fills with water at a constant rate. At…

A: Given: An inverted conical tank 10 m high and 3 m radius at the top fills with water at a constant…

Q: 2) A kite is flying at a fixed height of 30 ft. If 50 feet of string is out already from the spool,…

A: Given- A kite is flying at a height of 30 feet, if 50 feet of string is out already from the spool…

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: A triangle has a base that is decreasing at a rate of 4 cm/s with the height being held constant.…

A: Let b and h be the base and height of the trianglegiven rate at which base is decreasing, dbdt=4cm/s…

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

A: To determine the change of rate of the volume of cylinder.

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

A: Given: -

Q: A horizontal trough is 16m long, and its ends are isosceles trapezoids with an altitude of 4m, a…

A: The derivative is also called the rate of change of a quantity with respect to time. The volume of a…

Q: A rectangle is growing in such a way that when its length is 5 ft and its width is 2 ft, the length…

A:

Q: All the edges of a cube are expanding at a rate of 1/6 cm/sec. Determine the rate of change of the…

A: