The volume of the sphere is increasing at the rate of 6 cm?/hr. At what rate is its surface area increasing (in cm?/hr) when the radius is 50 cm? (А) 0.50 В) 0.30 0.40 D 0.24

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: The linear density of a rod 3m long at a point x meters from one end is ke-3x kilograms per meter.…

A: Solution is given below:

Q: A pebble is dropped into a calm pond, causing ripples in the form of concentric circles. The radius…

A: Rate of Radius of outer ripple increasing = 1 ft/sec                    Radius = 4 feet

Q: The sides of a square increase in length at a rate of 3 m/sec. a. At what rate is the area of the…

A: lets the size of square is l so the rate of change of length = dl/dt = 3 m/sec area of square = l2…

Q: Air is being pumped into a spherical balloon at a rate of 5 cubic centimeters per minute. Determine…

A: Given : The air is pumped into a balloon at a rate of 5 cm3/min The diameter of the balloon is 20 cm

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: Water is flowing at the rate of 9 ft3/min into a tank that is in the shape of a right circular…

A: Let r be the radius of base of cylinder, then r=2 ft .Let h be the height of water level at any time…

Q: A cube’s surface area increases at the rate of 72 in2/sec. At what rate is the cube’s volume…

A: Given:

Q: Water is being poured at the rate of 2z m' /min into an inverted conical tank that is 12-meter deep…

A: We need to find rate of water leaking.

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: The volume of a cube is increasing at the rate o 8 cm³/sec.How fast is the surface area increasing…

A:

Q: Water flows at the rate of 2000 cibic cm per second into a verical cylindrical tank 120 cm in…

A: Given: Water flows at the rate of 2000 cubic cm per second into a vertical cylindrical tank 120 cm…

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

A:

Q: The lateral area of the right circular cylindrical water tank is 92 sq m and its volume is 360 cubic…

A: Let's find.

Q: The original 24 m edge length x of a cube decreases at the rate of 3 m/min. a. When x = 4 m, at what…

A:

Q: Rain is falling into a cylindrical barrel at the rate of 20 cm3/min. If the radius of the base is 18…

A: Given,            Rain is falling into a cylindrical barrel at the rate of 20 cm3/min.…

Q: Air is escaping from a spherical balloon at the rate of 2cm per minute. How fast is the radius…

A: V=43πr3

Q: A spherical balloon is being deflated at a rate of 80 cm³/min. At what rate is the radius decreasir…

A:

Q: A water tank has the shape of an inverted circular cone with base radius 2 m and height 4 m. If…

A:

Q: A spherical snow ball is being made so that its volume is increasing at the rate of 8 ft /min. What…

A: given: dVdt=8 ft3 /min We have to find drdtwhen diameter of snowball is 4 ft i.e, radius= 2ft we…

Q: The side of a cube is increasing at a rate 7m/s, then the rate at which the volume of the cube…

A: Let s be the side of the cube in meter and V be the volume of the cube and t be the time in…

Q: 3. Find the cost of painting (overall) at the rate of P7.50 per sq. cm. a conical spire 40 cm radius…

A: As per our guidelines we are supposed to do only first question among multiple questions. To get the…

Q: Water is flowing at the rate of 6 ft/min into a tank that is in the shape of a right circular…

A: Given data:   The rate at which water is flowing in the cylindrical tank is dV/dt =6 ft3/min. The…

Q: side

A: Please refer to the image below

Q: A capacitor has two parallel metal plates measuring 0.45 m² each. The distance between the plates is…

A: Given:-Area of plates=0.45 m2distance between plate, d=1 cm=10-2mthickness of permittivity ,…

Q: The original 24 m edge length x of a cube decreases at the rate of 5 ​m/min.   a. When x=5m, at what…

A:

Q: Find the surface area of a sphere at the instant when the rate of increase of the volume of the…

A:

Q: Rain is falling into a cylindrical barrel at the rate of 20 cm3 /min. If the radius of the base is…

A:

Q: The volume of a cube is increasing at the rate of 8 cm /sec.How fast is the surface area in creasing…

A: We can find the answer as below

Q: gas is escaping a spherical ballon at the rate of 4cm per minute . how fast is the surface area…

A: Given that, Gas is escaping a spherical balloon at the rate of 4 cm per minute. The objective is to…

Q: Find the rate of change of volume of a sphere with respect to its surface area when the radius is 2…

A:

Q: Find the approximate change in the volume V of a cube of side x meters caused by increasing the side…

A:

Q: A conical paper cup is 30 cm tall with a radius of 10 cm. The bottom of the cup is punctured so that…

A:

Q: spherical balloon is inflated with gas at a rate of 900 cubic centimeters per minute.

A: Volume of the sphere is V=43πr3where r = radius of the sphere

Q: A spherical snowball is made so that its volume is increasing at a rate of 8 cubic feet oer minute.…

A: I set these up this way. what do we know?  dVdt= 8 ft 3/min What do we want?  drdt = ?   when d = 4…

Q: The volume of a cube is increasing at a rate of 68 in3/sec. At what rate is the length of each edge…

A: Related rates of changes –                 The related rate of change is finding the rate of change…

Q: The two equal sides of an isosceles triangle with fixed base b are b are decreasing at the rate of 3…

A: Solution :-

Q: 11. At what rate is the volume of the cube changing if the edge is 8 cm and is changing at 4 cm/s?

A: As we know that; The expression for the volume of the cube with the edge length ''a'' is: v=a3…

Q: The volume of a cube is growing at a rate of 2 in3/min. Determine the rate at which the surface of…

A: Given:The volume of a cube is growing at a rate of 2 in3/min, that is dVdt=2 in3/min, where V is the…

Q: Find the approximate change in the volume V of a cube of side x meters caused by increasing the side…

A:

Q: A wooden solid is made up of a cylinder with hemispherical ends. If the whole length of the solid is…

A: Radius of the cylinder, r = 7 cm Height of the Cylinder, h = (84 - 2r) cm…

Q: Water pours into a conical tank (an inverted cone) of height 10 m and radius 4 m at a rate of 6 m…

A: To find: The rate of water level rising when the level is 5 m high. Given: The height of the tank is…

Q: A bacterial cell is spherical in shape. If the radius of the cell is increasing at the rate of 0.01…

A: Volume of sphere: V = 43πr3, where r is radius of sphere. Surface area of sphere: S = 4πr2, where r…

Q: What is the differential form for the total surface area of a frustum of a cone with l as the slant…

A: The curved surface area of a frustum of a cone is:

Q: Air is being pumped into a spherical balloon at a rate of 4 cm3/min. Determine the rate at which the…

A:

Q: A spherical balloon is being inflated at the rate of 12m /min. If the radius of the balloon is 6m,…

A:

Q: Find the mass of a straight circular rod of length a and radius b whose density varies as the square…

A:

Q: 7, If a snowball melts so that its surface area decreases at a rate of 3 cm2/min, find the rate at…

A:

Q: A bacterial cell is spherical in shape. If the radius of the cell is increasing at the rate of 0.01…

A: Given , Bacterial cell is in spherical shape.Let radius be 'r' μm . ∴ Volume of cell, v v = 43π…

Q: Water flows at the rate of 2000 cubic cm per second into a vertical cylindrical tank 120 cm in…

A: Let height of cylindrical tank is "h". Diameter is 120 cm. So, Radius would be r=1202=60 cm Volume…