A spherical balloon is being inflated. Find the rate of increase of the surface area (S = 4xr²) with respect to the radius r when r is each of the following.(а) 4 ftft?/ft(b)5 ftft?/ft(c)8 ftft?/ft

Given, A spherical balloon is being inflated. surface area is S = 4πr²

A spherical balloon is being inflated. Find the rate of increase of the surface area (S = 4xr2) with respect to the radius r when r is each of the following. (a) 4 ft ft?/ft (b) 5 ft ft?/ft (c) 8 ft ft2/ft

A spherical balloon is being inflated. Find the rate of increase of the surface area (S = 4xr2) with respect to the radius r when r is each of the following. (a) 4 ft ft?/ft (b) 5 ft ft?/ft (c) 8 ft ft2/ft

Elementary Geometry for College Students

6th Edition

ISBN:9781285195698

Author:Daniel C. Alexander, Geralyn M. Koeberlein

Publisher:Daniel C. Alexander, Geralyn M. Koeberlein

Chapter8: Areas Of Polygons And Circles

Section8.4: Cicumference And Area Of A Cicle

Problem 45E: The diameter of a carousel merry-go-round is 30ft. At full speed, it makes a complete revolution in...

See similar textbooks

Related questions

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

Q: A balloon is being inflated. If its volume increases at the rate of 5cm^3/sec, how fast is the…

Q: A spherical balloon is being filled with air at the constant rate of (2 cm3)/(sec). How fast is the…

A: Given that A spherical balloon is being filled with air at the constant rate of (2 cm3)/(sec). This…

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

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

A: Rate at which surface area increases is

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

Q: A spherical balloon is inflated with air at a rate of 32 cm3/ min. At what rate does the radius…

A: Find dr/dr.

Q: A spherical balloon is inflating at a rate of 277T in³/sec. How fast is the radius of the balloon…

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: What is the rate of change of the area of acircle (A = pai r2) with respect to the radius when the…

A: The radius of a circle is r=3 units. The formula for area of circle is given by A=πr2

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

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

Q: The radius r of a circle is changing at the rate of -2/π m/sec. At what rate is the circle’s area…

Q: The radius R of a circle is increasing at the rate of 1 cm per sec. How fast is the area changing…

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

Q: What is the rate of change of the volume of a ball (V = (4/3)pai r3 ) with respect to the radius…

Q: A spherical balloon is being inflated at the rate of 12m3 /min. If the radius of the balloon is 6m,…

Q: A spherical balloon is being inflated. Find the rate of increase of the surface area (S = 47r2) with…

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: Assume a circle is expanding with time, where r = t + 2. What is the formula for the rate of change…

A: Given: r = t + 2 We know that the area of the circle: A = π r2 where r is radius.

Q: find the rate of change of the circumference of a circle when the area is increasing at the rate of…

A: Given: Rate of change of area is increasing at the rate of 4 cm2/sec, that is, dAdt=4 cm2/sec. To…

Q: The radius of a star(spherical) was r=a and was observed to increase by 0.01%. Use a linear…

A: Given data is : Radius(r) of a star (spherical) is increase by 0.01% To find the percentage of…

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: If a hemisphere bowl of radius 6 cm contains water to a depth of x cm, the volume of the water is rx…

A: This question is related to application of derivatives.

Q: Sand is leaking through a small hole at the bottom of a conical funnel at the rate of 12rcm³ / s. If…

A: Given: Radius of the funnel r=8 cm. Height of the funnel h= 16 cm. rate of change of volume…

Q: The radius of a circle is changing atthe rate of -2/paiA m/sec. At what rate is the circle’s area…

A: Let the radius of the circle be r. Then the area (A) of the circle is: A=πr2 Differentiating with…

Q: The volume of a metal in a hollow spherical is constant. If the inner radius is increasing at thr…

Q: Water is running out of a conical funnel at the rate of 1 in3/sec. If the radius of the base of the…

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

Q: ce of a circle is increasing at a rate of 2 cm/s. rea increasing when r= 6 cm?

A: We have to choose the correct answer from the given options according to the given information

Q: . A 13-ft ladder is leaning against a house when its base is 12 ft from the house, the base is…

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

A: The surface area is

Q: A yellow balloon, spherical in shape is inflated with a rate of 100 cm3 /sec. Calculate the rate at…

A: Given

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

Q: An inverted conical tank is being filled with water at the rate of 2ft3 per minute. If the tank has…

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

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

Q: A man walks along a straight path at a speed of 4ft/s. A spotlight is located on the ground 20ft…

Q: Sand is leaking through a small hole at the bottom of a conical funnel at the rate of 12rcm³ /s. If…

A: Given- dVdt=12π cm3sec.,R=8 cm and H=16 cm To find- depth of sand after 15seconds and the rate of…

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

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

Q: The spherical balloon is being filled with air at the constant rate of ( 2cm3 ) / (sec). How fast…

A: Given: The spherical balloon is being filled with air at the constant rate of 2cm3/sec We know that,…

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

A: Solution

Q: Water is falling on a surface, wetting a circular area that is expanding at a rate of 10mm^2/s. How…

Q: The radius of a circle is increasing at a rate of 2cm/s. How fast is the area of the circle…

Q: A snowball is being made so that its volume is increasing at the rate of 8 ft3/min. Find the rate at…

A: The geometrical figure of a snowball is a sphere. The volume of a sphere of radius r is V=4/3×πr3.…

Question

A spherical balloon is being inflated. Find the rate of increase of the surface area (S = 4xr²) with respect to the radius r when r is each of the following.
(а) 4 ft
ft?/ft
(b)
5 ft
ft?/ft
(c)
8 ft
ft?/ft

Expert Solution

This question has been solved!

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

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step by step

Solved in 4 steps with 3 images

SEE SOLUTION Check out a sample Q&A here