The volume V=r° of a spherical balloon changes with the radius. a. At what rate (ft°/ft) does the volume change with respect to the radius when r= 3 ft? b. Using the rate from part a, by approximately how much does the volume increase when the radius changes from 3 to 3.2 ft?

The volume V=r° of a spherical balloon changes with the radius. a. At what rate (ft°/ft) does the volume change with respect to the radius when r= 3 ft? b. Using the rate from part a, by approximately how much does the volume increase when the radius changes from 3 to 3.2 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

Section8.5: More Area Relationships In The Circle

Problem 42E: A goat is tethered to a barn by a 12-ft chain. If the chain is connected to the barn at a point 6 ft...

See similar textbooks

Related questions

Q: Given OZ with tangents XW and XY , what is MWVY ? (10a) (4a + 10)°, 70° X. W O A. 70 В. 140 C. 250 O…

A: Given <WY = (4a+10)° <WXY = 70° m<WVY = (10a)° We know that <WY+m<WVY =…

Q: A car is traveling at 50 mi/h when the brakes are fully applied, producing a constant deceleration…

A: A car is traveling at 50 mi/h when the brakes are fully applied, producing a constant deceleration…

Q: An engineering student is experimenting on a cylindrical can with a fixed rate of 8 inches. Find the…

A: Please check step 2 for the solution.!

Q: A water tank has a shape of an cylinder with a base radius of 4 m and a height of 24 m. If water is…

A: Given

Q: A Conical Cup is 4cm across and 6cm deel. Water leaks cut of the bottom of the cup cit a rate of…

A: Consider the given information. The diameter of the cup is 4 cm. r=d2=42=2 cm The height is 6 cm.…

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

Q: If water is pumped out at a rate of 5.2 L per second, how long will it take (in hours) to lower the…

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

A: given that radius of a sphere increases at a rate of 3m/sec find the rate when radius is 9m

Q: The volume V = (4/3)pai r3 of a spherical balloon changes with the radius. a. At what rate (ft3/ft)…

Q: The radius of a circle is decreasing at a rate of 3 cm/sec. At what rate is the area of the circle…

A: The radius of a circle is decreasing at a rate of 3 cm/sec. At what rate is the area of the circle…

Q: the measure of ∠L=90°, JL = 60, KJ = 61, and LK = 11. What ratio represents the tangent of ∠J?

Q: A hiker travels 4 mph at a bearing of S35°E from their campsite. After 3 hours, how far south is the…

A: A hiker travels 4 mph at a bearing of S35°E. The hiker moves in a direction away from due south…

Q: Coffee is draining out of a conical filter at a rate of 2.25 in³/min. If the cone is 4 in all and…

A: The volume of cone is given by . The rate of coffee draining is 2.25 cubic inch per minute. This…

Q: The clepsydra, or water clock, was a device that the ancient Egyptians, Greeks, Romans, and Chinese…

A: The water dripping out of the cylindrical container is modelled by a differential equation.…

Q: An object is launched at an angle of 50 degrees from the horizon at an initial velocity of 500 ft…

A: Given data: Formula used :

Q: A car is traveling at 50 mi/h when the brakes are fully applied, producing a constant deceleration…

A: Kinematic equation of velocity: (v2 - u2)=2as Where v=final velocity of car And u=initial velocity…

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

Q: The radius of a sphere increases at a rate of 2m/sec. Find the rate at which the surface area…

A: R=8 Dr/dt=2

Q: The tires of a bicycle have radius 13.0 in. and are turning at the rate of 215 revolutions per min.…

A: Angular velocity is calculated by v=rω where angular velocity represented by ω and linear velocity…

Q: The radius of a sphere increases at a rate of 2m/sec. Find the rate at which the surface area…

A: In sphere Rate of radius= 2m/s Find the rate of change in surface area?

Q: The radius of a circle is increasing at a rate of 4 ft/min. At what rate is its area changing when…

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

A: Solve it

Q: A ladder 10ft long rests against a vertical wall. If the bottom of the ladder slides away from the…

A: Let x be the distance between the base of the wall and the bottom of the ladder. And let θ be the…

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

Q: The velocity, in feet per second, of a running rodent is modeled by v(t) = 5√t − 2t. What is the…

Q: A pendulum of length 100.10 in., located at a point at sea level where the radius of the earth is R…

Q: A car is traveling at 68 ft/s when the brakes are fully applied, producing a constant deceleration…

A: Given, speed of car and deceleration

Q: hen the distance of the plane from at the rate of 8,000 km/hr. At w

A: Given: Perpendicular distance between station and plane is 5,000 km. To find rate of distance of…

Q: Find the unit rate of the statement given In the first column and match them with their approprlate…

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

Q: The radius of a sphere increases at a rate of 2m/sec. Find the rate at which the surface area…

Q: The volume V = (4/3)πr3 of a sphericalballoon changes with the radius.At what rate (ft3/ft) does the…

Q: The flow of blood in a blood vessel is faster toward the center of the vessel and slower toward the…

A: We have to find the rate of change in velocity of blood.

Q: The Cleveland City Cable Railway had a 14-foot-diameter pulley to drive the cable. In order to keep…

Q: be the angle between the top of the ladder and the wall and let x be the distance from the bottom of…

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

A: Use the concept of derivative and apply this on formula of surface area of sphere.

Q: Find the value of x given the radius and tangent AB. * A 40 B 30; O 40 O 50 O 60 O 70

A: We have given a circle with Radius, r = 30 Length of tangent AB = 40 As the point where tangent…

Q: The volume V = 3 "Tr° of a spherical balloon changes with the radius. 3 a. At what rate (in°/in)…

A: We know that the volume of the sphere is V=43πr3 To find the rate of change in volume with respect…

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

A: Surface area of sphere is S= 4πr^2. And rate of change means derivatives.

Q: A kite, 120 ft above the ground, is moving horizontally at a rate of 10 ft/sec. At what rate is the…

Q: For many species of fish, the allometric relationship between the weight W and the length L is…

A: Here the given that, the allometric relationship between the weight W and the length L is…

Q: Given OZ with tangents XW and XY, what is MWVY ? (10a) V (4a + 10)°, 70° X. O A. 70° B. 140° C. 250°…

Q: What is the tangent ratio for zB? C B V5 A 1,

A: With respect to angle B, here, Altitude, a=2 Base, b=1 Hypotenuse, h=5

Q: The sides of an equilateral triangle are increasing at the rate of 4 cm/s. At what rate is the area…

A: Let x cm be the length of the side of an equilateral triangle at any time t. Given that, dxdt=4…

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

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

Question

The volume V=r° of a spherical balloon changes with the radius.
a. At what rate (ft°/ft) does the volume change with respect to the radius when r= 3 ft?
b. Using the rate from part a, by approximately how much does the volume increase when the radius changes from 3 to 3.2 ft?

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

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Indefinite Integral$

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

In Exercises 41 and 42, round to two decimal places. A goat is tethered to a barn by a 12-ft chain. If the chain is connected to the barn at a point 6 ft from one end of the barn, what is the area of the pasture that the goat is able to graze?
Measure the lengths of g-k in Figure 30-26 to the nearer whole millimeter.
For Exercises 23 through 34, round the answers to 1 decimal place. 29. All dimensions are in millimeters. Find the shaded area of Figure 39-19. Area = dt+2a(s+n)
Solve these prism and cylinder exercises. Where necessary, round the answers to 2 decimal places unless otherwise specified. A cylindrical 1.000-liter vessel has a base diameter of 5.00 centimeters. How high is the vessel?