A spherical party balloon is being inflated with helium pumped in at a rate of 6 cubic feet per minute. How fast is the radius growing at the instant when the radius has reached 3 ft? HINT [SeeExample 1.] (The volume of a sphere of radius r is V =Round your answer to two decimal places.)ft/min

Answered: Image /qna-images/answer/096f7abd-458f-4bb0-b2ef-acae628bf657.jpg

Answered: Example 1.] (The volume of a sphere of…

Math

Calculus

Example 1.] (The volume of a sphere of radius r is V = -r. Round your answer to two decimal places.) ft/min

Mathematics For Machine Technology

8th Edition

ISBN:9781337798310

Author:Peterson, John.

Publisher:Peterson, John.

Chapter65: Achievement Review—section Six

Section: Chapter Questions

Problem 55AR: Solve these prism and cylinder exercises. Where necessary, round the answers to 2 decimal places...

See similar textbooks

Related questions

Q: A conical paper cup is 20 cm tall with a radius of 10 cm. The bottom of the cup is punctured so that…

A: NOTE: Refresh your page if you can't see any equations. . height of the cone s h=20 and the radius…

Q: e radius of a right circular cone having a lateral area of 544.12 m² to have a maximum volume.

A: In this question, the concept of maxima and minima is applied. Maxima and Minima The critical points…

Q: A composite figure is a cylinder with a hemispherical hole in the top. The bottom of the hemisphere…

A: The given figure is: Since the bottom of the hemisphere touches the base of the cylinder.…

Q: A spherical snowball is melting in such a way that its radius is decreasing at a rate of 0.3 cm/min.…

Q: The total amount of a cylinder inserted into a hemisphere of radius 1 unit What is the maximum value…

Q: Two equal sides of an isosceles triangle with fixed base b are decreasing at the rate of 3 cm / sec.…

Q: The radiusof an air bubble is increasing at the rate of 0.5cm/ sec At what rate if the volume of the…

A: Rate of change

Q: 12. The height of a right circular cone is increasing at 3mm/s and its radius is decreasing at…

A: Volume of a right circular cylinder is given by formula, V=πr2h , where r is the radius of circular…

Q: A solid is formed by adjoining two hemispheres to the ends of a right circular cylinder. The total…

A: Since, a solid is formed by adjoining two hemispheres to the ends of a right circular…

Q: A coat of paint of thickness 0.5 mm is applied evenly to the surface of a sphere a radius 20 cm.…

Q: The linear density in a rod 2 m long is 2xe-x^2 kg/m, where the x is measured in meters from one end…

Q: A cylinder is inscribed in a right circular cone of height h and radius (at the base) equal to r.…

A: Given, radius(r) and height(h) of cone

Q: Water is flowing at the rate of 50 m3/min from a shallow concrete conical reservoir (vertex down) of…

A: Water is flowing at rate of 50 m3/ min from a shallow concrete conical reservoir of base radius 45 m…

Q: A vessel in the shape of a cone has a height of 48 cm and a base diameter of 16 cm. It holds water…

Q: A tank, shaped like a cone has height.10 meters and base radius 3 meters long. It is placed so that…

A: We have to find work done to pull out all water from tank.

Q: A solid is formed by adjoining two hemispheres to the ends of a right circular cylinder. The total…

A: Given A solid is formed by adjoining two hemispheres to the ends of a right circular cylinder. The…

Q: A tank, shaped like a cone has height 10 meters and base radius 3 meters long. It is placed so that…

A: please refer to the image below

Q: Water is leaking out of an inverted conical tank at a rate of 7500 cubic centimeters per min at the…

A: In this we have to follow some basic concepts so for better understanding I'm providing hand written…

Q: A cylinder is inscribed in a right circular cone of height 5 and radius (at the base) equal to 5.5.…

A: Let the height of the cylinder is h and radius is r. The cylinder in inscribed in the cone of height…

Q: A vessel in the shape of a cone has a height of 48 cm and a base diameter of 16 cm. It holds water…

A: Given, Height of cone= 48 cm Base diameter = 16 cm Radius of cone = 8 cm Depth of water = 18 cm…

Q: A solid is 3 m high. The cross-section of the solid at height x meters above its base has area 2z…

A: Volume is equal to base area multiolied by height.

Q: 21. The radius of a spherical balloon is increasing at the rate of 3 centimeters per minute. How…

Q: The original 24 m edge length x of a cube decreases at the rate of 3 m/min. a. When x = 1 m, at what…

Q: 5. A spherical balloon is inflated so that its volume is increasing at the rate of 2 m'/min. At what…

A: Let r be the radius of the balloon and D be the diameter.

Q: 4. Using differential, determine the error in computing the volume of a cube if the error in…

A: Error in volume

Q: The radius of a right circular cone is increasing at a rate of 1.5 in/s while its height is…

Q: Volume with respect to time when r = 15 cm

A: Given the radius of a sphere is expanding at a rate of 30cm/min i.e. dr/dt=30 Given volume of sphere…

Q: A cylinder is inscribed in a right circular cone of height 2.5 and radius (at the base) equal to 5.…

Q: A trough has an open top 0.30 m by 6 m and closed vertical ends which are equilateral triangles 30…

A: Given: The trough with following specification To find: The volume of the cater hold if filled half…

Q: A certain pine tree maintains the shape of a cone. When the base of the tree is 28 ft in diameter,…

Q: Water is leaking out of an inverted conical tank at a rate of 10,000 cm3/min at the same time that…

Q: A cylindrical can, open at the top, is to hold 800 cm³ of liquid. Find the height, h, and the…

A: As we know that the volume of the cylinder is: v=πr2h Given: v=800cm3 So, 800cm3=πr2hh=800πr2....(1)…

Q: A cylinder is inscribed in a right circular cone of height 5.5 and radius (at the base) equal to 6.…

A: Please see the white board for the pictorial depiction of the question.H = height of the right…

Q: 3. A container in the shape of a right circular cylinder with no top has surface area 3n ft2. What…

Q: 1. A pebble is dropped in a calm pond causing ripples in the form of concentric circles. The radius…

Q: A right circular cone with radius 'r' is inscribed in a sphere with radius 'R. If it is known that,…

Q: A spherical snowball is melting in such a way that its radius is decreasing at a rate of 0.1 cm/min.…

Q: A sphere of radius 5 cm is lowered into a rectangular tank 50 cm long and 20 cm wide containing…

Q: A solid is formed by adjoining two hemispheres to the ends of a right circular cylinder. The total…

A: total vol. of solid = 43πr3+πr2hwhere r=radius of cylinder and sphereh=height of cylinderGiven that…

Q: A manufacturer is making cylindrical cans that hold 300 cm. The dimensions of the can are not…

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 colony of bees lives in an ever-growing beehive that is in the shape of a sphere. Use The volume…

A: 20 new bees are added to the hive each week. Each bee in the colony needs 5 cm3 of space. (space…

Q: A solid is formed by adjoining two hemispheres to the ends of a right circular cylinder. The total…

Q: 22. Identify the volume generated by revolving one arch of the sine curve about the x-axis.

Q: A spherical balloon is to be deflated so that its radius decreases at a constant rate of 10 cm/min.…

A: Given: Radius decreases at a rate of 10 cm/min drdt=-10 To find dvdt when r=10

Q: A solid is formed by adjoining two hemispheres to the ends of a right circular cylinder. The total…

A: solid = one cylinder + 2*semi-sphere

Q: A tank, with a rectangular base measuring 10 cm ☓ 20 cm is 1/3 filled with water to a depth of 18…

Q: Express

Q: A certain gas expands to fill a 3 L container. Its mass is measured to be 0.6 kg. What is its…

Question

A spherical party balloon is being inflated with helium pumped in at a rate of 6 cubic feet per minute. How fast is the radius growing at the instant when the radius has reached 3 ft? HINT [See
Example 1.] (The volume of a sphere of radius r is V =
Round your answer to two decimal places.)
ft/min

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Spheres$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Similar questions

Solve these prism and cylinder exercises. Where necessary, round the answers to 2 decimal places unless otherwise specified. A solid right cylinder 9.55 centimeters high contains 1910 cubic centimeters of material. Compute the cross-sectional area of the cylinder.
Solve these prism and cylinder exercises. Where necessary, round the answers to 2 decimal places unless otherwise specified. Compute the height of a prism with a base area of 2.7 square feet and a volume of 4.86 cubic feet.
Solve these prism and cylinder exercises. Where necessary, round the answers to 2 decimal places unless otherwise specified. Compute the base area of a right circular cone that is 15.8 centimeters high and has a volume of 1070 cubic centimeters.
Solve these prism and cylinder exercises. Where necessary, round the answers to 2 decimal places unless otherwise specified. Compute the volume of a prism with a base area of 220.0 square centimeters and a height of 7.600 centimeters.
Solve these prism and cylinder exercises. Where necessary, round the answers to 2 decimal places unless otherwise specified. Find the volume of a right circular cylinder that has a height of 4,600 inches and a base area of 53.00 square inches.
Solve these prism and cylinder exercises. Where necessary, round the answers to 2 decimal places unless otherwise specified. The frustum of a right circular cone has a larger base area of 40.0 square centimeters and a smaller base area of 19.0 square centimeters. The height is 22.0 centimeters. Find the volume. Round the answer to the nearest cubic centimeter.
Solve these exercises. Where necessary, round the answers to 2 decimal places unless otherwise specified. Find the base diameter of a right circular cone that has a volume of 922.4 cubic centimeters and a height of 14.85 centimeters.