If the radius of a sphere is increasing at a constant rate of 2 cm/sec, then the volume 3 is increasing at a rate of cm°/sec when the radius is 4 cm.

Q: A spherical snowball melts at a rate of 36π^2in³/sec. At what rate is the radius of the snowball…

A:

Q: An engineer is experimenting with a cylindrical can with a fixed height of 15 in. Find the rate of…

A: GIVEN-  A CYLINDER OF HEIGHTS 15 inch is given AND RADIUS =4 inch TO FIND -  RATE OF CHANGE OF…

Q: If a snowball melts so that its surface area decreases at a rate of 1cm /min, find the rate at which…

A: Diameter= DRadius = r =D/2Surface area = A= 4pi*r^2Given dA/dt= -1 cm^2/min (negative because…

Q: A spherical balloon is to be deflated so that its radius decreases at a constant rate of 5 cm/min.…

A:

Q: The radius of a sphere decreases at a rate of 1 m/se decreases when the radius is 15 m

A:

Q: A spherical balloon is to be deflated so that its radius decreases at a constant rate of  6cm/min.…

A:

Q: A pulley having a diameter of 36 cm is turned by a belt that moves at the rate of 5 m/sec. How many…

A: In one revolution the pulley will rotate by an angle of 360°. Hence, the belt will cover a distance…

Q: A water tank has the shape of an inverted circular cone (point down) with a base of radius 6 feet…

A: We can consider two similar triangles from the question and using that we can make an expression for…

Q: Water is poured into a conical paper cup at the rate of 3/2 in3/sec (similar to Example 4 in Section…

A: The situation is as shown below: Consider a small differential element of water at a height of h…

Q: Suppose that a given moment, the radius of a right circular cylinder is 2 cm and increasing at a…

A:

Q: if the base of triangle is constantly 4 cm find the rate at which the area of the triangle is…

A:

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: If the volume of a cube is decreasing at a rate of 24 in sec, then find the rate at which the length…

A:

Q: A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the…

A: To find: The rate at which the angle between the ladder and the ground  is changing

Q: A trough of water is 8 meters in length and its ends are in the shape of isosceles triangles whose…

A: Given:- A trough of water is 8 meters in length and its ends are in the shape of isosceles triangles…

Q: If a ball of candy is covered in chocolate and is melting so that its surface area decreases at a…

A: To find: The rate at which diameter decreases when diameter is 10 cm. Given: The rate of surface…

Q: A spherical balloon has a radius r that is increasing at a rate of 3 cm/s. At what rate is the…

A:

Q: A 25-ft ladder is leaning against a wall. If the bottom is pulled away from the wall at a rate of 5…

A:

Q: The surface area of a sphere increases at a rate of 90 m/sec. Then the rate at which the radius…

A:

Q: Water is being released from a conical reservoir (vertex down) 20 ft in radius and 40 ft deep at a…

A: Use similar triangle to shoe that  r/20 = h/40 where r and h are the radius and height of water in…

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

A: The rate of increase of the width of a rectangle i.e. dwdt=2 cm/sec The rate of increase of the…

Q: Question 4

A: Let a be the acceleration, v be the velocity, s be the position and t be the time of braking.

Q: The surface area of a sphere increases at a rate of 55 m²/sec. Then the rate at which the radius…

A:

Q: 10. At what rate is the vertex angle of a right circular cone changing when the radius is 3 ft and…

A:

Q: If the rate of change of the surface area of a sphere with respect to its radius is 16pi sq cm, find…

A:

Q: Water is flowing into a vertical cylindrical tank at the rate of 5 cu ft/min. If the radius of the…

A: Given, water is flowing into a vertical cylindrical tank at the rate of 5 cu ft/min (ie) Volume is…

Q: A light is on the top of a 12 ft tall pole and a 5 ft 6 inches tall person is walking away from the…

A:

Q: 3.) A conical tank is 10ft across the top and 12 ft. deep. If oil is poured into the tank at the…

A:

Q: 1. A car is travelling at 50 mi/hr when the breaks are fully applied, producing a constant…

A:

Q: A vertical cylinder is leaking water at a rate of 8m^3/sec. if the cylinder has a height of 10m and…

A: In a vertical cylinder water is leaking at a rate of 8 m3/sec. dVdt=8 Height of the cylinder is 10…

Q: The volume of a cube increases at a constant rate of 135 ft°/ sec. The rate at which the side of the…

A:

Q: 1. Water is flowing into a vertical cylindrical tank at the rate of 24 cu. ft. per min. If the…

A: Given , Water is flowing into vertical tank at rate if 24 cu .ft . per min. Radius of tank is 4ft.…

Q: 3) If a spherical snowball melts so that its surface area decreases at a rate of 1 cm? he rate at…

A: It is given that a spherical ball melts so that its surface area decreases at a rate of 1 cm2 per…

Q: A spherical balloon is to be deflated so that its radius decreases at a constant rate of 15 cm/min.…

A:

Q: The volume of a sphere is increasing at a rate of 40 cm^3/sec. At what rate is the radius ofthe…

A:

Q: If the radius of a sphere is increasing at a constant rate of 3 cm/sec, then the volume is…

A:

Q: A ladder 20 feet long is leaning against an embankment inclined 60 degrees to the horizontal. if the…

A: The ladder is leaning against an embankment inclined 60 degrees to the horizontal has length 20…

Q: A kite, 120 ft above the ground, is moving horizontally at the rate of 10 ft/sec. At what rate is…

A:

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

A: From the given information, draw a picture.

Q: A spherical balloon is being inflated at a rate of 9(pi)cm^3/sec. At what rate is its radius…

A:

Q: A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the…

A: To determine the rate of change of angle between the ladder and the ground.

Q: A cube is expanding in such a way that the length of its diagonal is increasing at a rate of 5…

A: Let y be the diagonal, x be the length of an edge and V be the volume of the cube at any time t.…

Q: If a spherical balloon is being filled with air at a constant rate of 2 cm³/s, at what rate is the…

A: Let r be the radius of the balloon in cm and V be the volume in cm3. The variable t stands for time…

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: . A vertical cylinder is leaking water at a rate of 1 ft /sec. If the cylinder has a height of 10 ft…

A:

Q: A 15-ft ladder is leaning against a wall. If the bottom is pulled away from the wall at a rate of 3…

A:

Q: The radius of a sphere decreases at a rate of 4 m/s. when the radius is 7 m, then the rate at which…

A:

Q: Assume a spring is oscillating and the length of the spring can be described as sin (t) L (t)=- What…

A: