Air is being pumped into a spherical balloon so that it volume increases at a rate of 100 cubic cm / s. How fast is the radius of the balloon increasing when its diameter is 50 cm.?

Q: A balloon is being inflated by pumped air at the rate of 2 cubic inches per second. How fast is the…

A: Given: Rate at which air is pumped in the balloon=2 cubic inches per second……1   To find: Rate of…

Q: Suppose that the sides of a cube are expanding at a rate of 2 inches per minute. How fast i the…

A: We need to find the rate of change of volume of cube when side is 20 inches. Volume of cube=(side)3…

Q: A spherical balloon is inflated at a rate such that it's radius increases at a rate of 500…

A: rate of change in volume = 307876.08 detailed solution with explanation is given below

Q: a. Air is being pumped into a spherical ball in such a way that the volume increases at a rate of 10…

A: Given: Volume of sphere is increasing at a rate of 10 cm^3/sec.

Q: A 10​-foot ladder is leaning against a vertical wall​ when Jack begins pulling the foot of the…

A: The given data can be expressed in a right triangle as shown below.

Q: The volume of a right circular cylinder is 60 cm3 and is increasing at 2 cm3/min at a time when the…

A: First we have to differentiate expression of volume with respect to time.

Q: Sugar is poured into a conical tank at the rate of 15cm3/sec whose bottom radius is always quarter…

A: The volume of a cone is given by the formula V=13πr2h. Where, V-volume, r-radius and h is the height…

Q: A spherical balloon is inflating with helium at a rate of 192n ft° / min. How fast is the balloon's…

A: V=43πr3S=4πr2

Q: The radius of a sphere is increasing at a rate of 3 mm/s. How fast is the volume increasing when the…

A:

Q: The radius of a sphere is increasing at a rate of 2 mm/s. How fast is the volume increasing when the…

A: Given that the diameter= 100 mm So the radius is=r=1002=50 mm Given that the radius of a sphere is…

Q: A hand-tossed pizza crust starts off as a ball of dough with a volume of 400πcm^3. First, the cook…

A:

Q: A 25-foot ladder is leaning against a wall and the base begins to fall away from the wall. When the…

A: A 25-foot ladder is leaning against a wall and the base begins to fall away from the wall. When the…

Q: A spherical balloon is inflated with gas at a rate of 10 cubic metres per minute. How fast is the…

A:

Q: The radius of a sphere is increasing at a rate of 4mm/s. How fast is the volume increasing when the…

A: The rate of change of the radius of the sphere, drdt = 4 mm/s To evaluate : The rate at which the…

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Q: Oil from an uncapped well is radiating outward in the form of a circular film on the surface of the…

A: Let r and A be the radius and area of the circle respectively at time t. The radius of the circle is…

Q: A 6-ft-diameter cylindrical tank is filled with water to a height of 10 ft. It is drained such that…

A:

Q: A cylindrical tank of radius 10 feet is being filled with wheat at the rate of 314 cubic feet per…

A: consider the radius of a cylindrical tank by r. The volume of a cylindrical tank is given as V. The…

Q: Air is being pumped into a sperical balloon so that its volume increases at a 12. rate of 16 cubic…

A:

Q: Liquid is escaping from a conical funnel at the rate of 3 cm3 /min. If the top of the funnel has a…

A: Given, r= 4 cm h= 20 cm dV/dt= 3 cm³/min Therefore, r/h= 4/20= 1/5 r= h/5

Q: A spherical balloon is being inflated at a rate of 20 cubic centime- ters of air per second. How…

A: We will use chain rule and the information provided.

Q: Water runs into a sunken concrete hemi- spherical bowl of radius 5 m at the rate of 0.2 m3/sec. How…

A: The derivative gives the rate of change of some variable with respect to other quantity. If a…

Q: A spherical balloon is inflated so that its volume is increasing at the rate of 7 ft^3/min. How fast…

A: given: A spherical balloon is inflated so that its volume is increasing at the rate of 7 ft^3/min.…

Q: The radius of a sphere is increasing at a rate of 5 mm/s. How fast is the volume increasing when the…

A: Let be the volume and r be the radius of the sphere respectively.

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

A: Let r be the radius of spherical ballon

Q: The radius of a sphere is increasing at a rate of 4 mm/s. How fast is the volume increasing when the…

A: Volume of sphere= =43πR3 where R is the Radius of the sphere.

Q: A snowball is melting at a rate of 2.4ft^3 hr^-1 – if the snowball remains a sphere throughout the…

A: given: A snowball is melting at a rate of 2.4ft3/hr. that implies dVdt=-2.4ft3/hr where V is the…

Q: A conical reservoir is losing water at the rate of 12 cubic feet per minute. If the radius is % the…

A: Let the height of the conical reservoir be h. Then the radius will be = h/4 Therefore we get the…

Q: A cylindrical tank with a radius of 5 m is being filled with water at a rate of 3m^3/min. How fast…

A:

Q: A spherical balloon is increasing in volume at 24t Cm . How fast is the radius ст S. of the balloon…

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Q: Air is pumped into a spherical balloon at the constant rate of 200 cubic centimeters per second. How…

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Q: An artist paints a portrait on a circular canvas and encloses it in a circular metal frame. At a…

A: Let the radius of the circular canvas be r.   The area of the canvas will be given by: A=πr2   Also,…

Q: The radius of a sphere is increasing at a rate of 4 mm/s. How fast is the volume increasing when the…

A:

Q: Air is pumped into a spherical balloon so that its volume increases at a rate of 100 cm /s. How fast…

A: d[r^n]/dr = n r^(n-1)

Q: A spherical balloon is inflated so that its radius increases at a rate of cm/sec. How fast is the…

A: Volume of the sphere is given by:  V = 43πr3

Q: Suppose the radius of a sphere is expanding at a rate of 3 inches per minute. How fast is the volume…

A: Let V & r be the volume and radius of the sphere at any time t respectively. Given that, the…

Q: A 13-ft ladder is leaning against a house when itsbase starts to slide away. By the time thebase is…

A: If a ladder is leaning against a wall and when its base starts to slide away it makes a triangle…

Q: How fast is the volume of a cube changing when the edge is 15 cm if the edge is changing at the rate…

A:

Q: A spherical balloon is being inflated. The volume is increasing at a rate of 5 mm per second. How…

A: Given: The volume of a spherical balloon is increasing at the rate of 5 mm3/sec. The diameter of…

Q: A small balloon is released at a point 150 feet away from an observer who is on level ground. If the…

A: we have to find

Q: how

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Q: A cylindrical tank with radius 5m is being filled with water at a rate of 4 m^3/min. How fast is the…

A: Given:         radius of cylinder (r)=5m         rate of water filled dvdt=4m3/minwe know that…

Q: Suppose an elastic rubber band is used to make a square, and is being streched (while keeping the…

A:

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

A: Given that volume of a cube is increasing at the rate of 8cm3/sec find out the fastness in the…

Q: Air is being pumped into a spherical balloon so that its volume increases at a rate of 50 cm3/s. How…

A: Let radius of the balloon is =r and diameter =d=30 cm It is given that Volume increases at rate…

Q: A 25 -foot ladder is leaning against a vertical wall​ when Jack begins pulling the foot of the…

A:

Q: Helium is pumped into a spherical balloon at a constant rate of 3 cubic feet per second. How fast is…

A:

Q: The radius of a sphere is increasing at a rate of 4mm/s.How fast is the volume increasing when the…

A: Given that the radius of a sphere is increasing at a rate of 4mm/s. That is, Now consider the…