2. A balloon in the shape of a sphere is being inflated at the rate of 100 cm/sec. a. At what rate is the radius of the sphere changing at the instant the balloon reaches 16 cm in diameter? b. At what rate is the surface area of the sphere changing at the instant the balloon reaches 16 cm in diameter?

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

A:

Q: A spherical balloon is inflated and its volume increases at a rate of 30 in3 /min. (a). What is the…

A: Given that, The spherical balloon is inflated and its rate of change of volume is; dVdt=30 (in3min)…

Q: The legs of an isosceles right triangle increase in length at a rate of 2 m/s. a. At what rate is…

A:

Q: A baseball diamond is a square 90 ft on a side. A player runs from first base to second base at 15…

A: 6)

Q: 1. The side of a cube increases at the rate of 23 m/sec. Find the rate at which the volume of the…

A:

Q: A 10-ft ladder is leaning against a house when its base starts to slide away. By the time the base…

A: Given that, the length of the ladder is 10 ft and distance between the wall and ladder in base is 6…

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

A:

Q: If the radius of a sphere is increasing at a constant rate of 2 cm/sec, then the volume 3 is…

A:

Q: 2. A spherical snowball melts at a rate of 367T in /sec. At what rate is the radius of the snowball…

A:

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

A: I will use the formula V=13πr2h and differentiation method to solve this problem.

Q: 1. A paper cup has the shape of a cone with height 12 cm and radius 4 cm (at the top). If water is…

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: A 25-ft ladder is leaning against a house when its base starts to slide away. By the time the base…

A:

Q: The legs of an isosceles right triangle increase in length at a rate of 6 m/s a. At what rate is the…

A: Let, l be the length of a legth of a leg of an isosceles right triangle, h be the length of the…

Q: 2): The side of a cube decreases at a rate of 6 m/sec. Find the rate at which the surface area of…

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

A:

Q: A baseball diamond is a square 90 ft on a side. A player runs from first base to second base at 15…

A:

Q: Consider a pool shaped like the bottom half of a sphere, that is being filled. The radius of the…

A: The volume of hemisphere filled with liquid to height h = πrh2-π3h3

Q: The legs of an isosceles right triangle increase in length at a rate of 5 m/s. a. At what rate is…

A:

Q: How fast is the surface area of a circular oil spill in the ocean changing when the radius is 10ft…

A:

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: The radius of a sphere is increasing at the rate of 2 meters per se of change of the volume with…

A: Given: The radius of a sphere is increasing at the rate of 2 meters per second.

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

A:

Q: All edges of a cube are expanding at a rate of 3 centimeters per second. (a) How fast is the volume…

A:

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

A: Given

Q: The volume V of a right circular cone of radius r and height h is given by V = 1/3 πr2h. a) What is…

A: Simply take derivative with respect to given variable considering other as constant.

Q: 12) A vertical cylinder is leaking wader at a rate I ft3% If the cylinder har a height of 10t Sec.…

A: Volume of cylinder = πr2h  r= radius of cylinder  h= height of cylinder

Q: The legs of an isosceles right triangle increase in length at a rate of 6 m divided by s.a. At what…

A: Let x  be the length of leg and h be the length of hypotenuse of an isosceles right triangle. Then…

Q: 1.) Water is pouring into a conical vessel 15 cm deep and having a radius of 3.75 cm across the top.…

A: step by step clear explanation is given .Have a look

Q: Find the rate at which the volume of a right circular cylinder of constant altitude 10 ft changes…

A:

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

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: Imagine a sphere whose radius r increases at a rate of 3 cm/s. At what rate is the volume V of the…

A: Note the results : Volume of the sphere is 43πr3 . Suppose F is a function of x and x is a function…

Q: Suppose that a tumor in a person’s body has a spherical shape and that treatment is causing the…

A: we know that the volume of the sphere                       V=43πr3                          (1)

Q: A vertical circular cylinder has radius r ft and height h ft. If the height and radius both increase…

A:

Q: 1. The side of a cube increases at the rate of 12 m/sec. Find the rate at which the volume of the…

A: Our guidelines for multiple questions,answer only first question For other answers , Repost this…

Q: (2) In calm waters, the oil spilling from the ruptured hull of a grounded tanker spreads in all…

A:

Q: A conical cistern of height 5 ft and 7 ft across the top is being filled at a rate of 5 ft3/s while…

A: A conical cistern is given whose height is 5 ft and diameter at the top is 7 ft. A conical cistern…

Q: A 25-ft ladder is leaning against a house when its base starts to side way. By the time the base is…

A: Consider h is the height, and b is the base, ladder's length be 'L' apply the Pythagoras theorem,…

Q: 4. The radius of a sphere decreases at a rate of 3 m/sec. Find the rate at which the surface area…

A: Surface area of sphere is given by: A=4 π r2 Find the rate at which the surface area decreases when…

Q: 7. A vertical cylinder is leaking water at a rate of 1 ft'/sec. If the cylinder has a height of 10…

A: To find the rate of change of height of water changing

Q: 2. The volume of a cube decreases at a rate of 10m/sec. Find the rate at which the side of the cube…

A: dVdt=10m3/min, side=2mFormula of volumeV= side3

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    26    foot    ladder    is    sliding    down    a    vertical    wall.        The    base…

A: Consider a function y= f(x)  then the derivative f '( x) is the  rate of change of y with respect to…

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) In calm waters, the oil spilling from the ruptured hull of a grounded tanker spreads in all…

A: Solution