Answered: 5. [ | The radius of a sphere increases…

5. [ | The radius of a sphere increases at the rate of 5 m/sec. Find the rate at which the volume of a sphere increases when the radius is 12 m.

Mathematics For Machine Technology

8th Edition

ISBN:9781337798310

Author:Peterson, John.

Publisher:Peterson, John.

Chapter47: Applications Of Formulas To Cutting Speed, Revolutions Per Minute, And Cutting Time

Section: Chapter Questions

Problem 41A: Compute the following problems. Express the answers to 1 decimal place. Use: T=LFN A slot 812.00...

See similar textbooks

Related questions

Q: The side of a cube increases at the rate of 11 m/sec. Find the rate at which the volume of the cube…

A: givenside of cube(a)=5mdadt=11m/secVolume of cube (v)=a3differentiating with respect to…

Q: 1. The side of a cube decreases at a rate of 2.5m/s. Find the rate at which the surfacearea…

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

Q: The radius of a right circular cone is increasing at a rate of 1.2 in/s while its height is…

A: Differentiate volume wrt t

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

Q: 8. The radius of a sphere is increasing at a rate 4mm/s. How fast is the volume increasing when the…

A: Given that the radius of sphere is increasing at a rate 4mm/s. drdt=4mm/s To find the rate at which…

Q: 8. If a snowball melts so that its surface area decreases at a rate of 4 cm2 /min , find the rate at…

Q: 2. A balloon in the shape of a sphere is being inflated at the rate of 100 cm/sec. a. At what rate…

A: a) Given that the balloon is in the shape of sphere and it is being inflated at the rate of…

Q: 2)The radius of a sphere decreases at the rate of 1 m/sec. Find the rate at which the volume…

A: Given, The radius of a sphere decreases at the rate of 1 m/sec We have to find the rate at which…

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

Q: 11. A snowball melts so that its surface area decreases at a rate of 0.5 cm/min. Find the rate at…

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

Q: 8. The radius of an inflating balloon in the shape of a sphere is changing at a rate of 3cm/sec. At…

Q: 63. Prove that the rate of change of the volume of a spherewith respect to its radius r is equal to…

A: GIVEN the rate of change of the volume of a spherewith respect to its radius r is equal to the…

Q: 3. Water is flowing into a vertical cylindrical tank at the rate of 24 cubic ft. /min. if the radius…

Q: The radius of an bubble is increasing at the rate of 1/2 cm/s. At what rate is the volume of the…

A: Here radius of bubble is given and rate of change of radius of bubble is also given

Q: 4. A spherical snowball is being made so that its volume is increasing at the rate of 8 ft³ /min.…

A: Differentiate both sides of the equation, V=43πr3 with respect to t to establish a relation between,…

Q: 2) The radius of a sphere decreases at the rate of 2 m/sec. Find the rate at which the volume…

Q: 2. The radius of a sphere decreases at the rate of 5 m/sec. Find the rate at which the volume…

A: Given that the Radius of sphere decreases at the rate of 5m/sec and radius is 5 m

Q: The volume of a cube decreases at a rate of 12.1 m/sec. Find the rate at which the side of the cube…

A: we have to find the rate change of a side of cube

Q: 16. If the radius of a circle is increasing at the rate of 4 cm/s, find the rate of the increase in…

A: Given radius of a circle is increasing at the rate of 4 cm/sec.

Q: 2)The radius of a sphere decreases at the rate of 4 m/sec. Find the rate at which the volume…

A: We need to find the rate at which volume decrease when radius is 3m

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: Suppose that a drop of mist is a perfect sphere and that, through condensation, the drop picks up…

Q: 3) If a spherical snowball melts so that its surface area decreases at a rate of 1 cm? he rate at…

A: It is given that a spherical ball melts so that its surface area decreases at a rate of 1 cm2 per…

Q: The volume of a sphere is increasing at a rate of 40 cm^3/sec. At what rate is the radius ofthe…

Q: 6. The radius of a right circular cylinder is increasing at the rate of 3in/sec, while the height is…

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

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

Q: 9. The radius of a sphere is expanding at a rate of 20 cm/min. Find the instantaneous rate of change…

A: The radius of a sphere is expanding at a rate of 20 cm/min. Find the instantaneous rate of change in…

Q: A spherical snowball is melting in such a way that its surface area decreases at the rate of 1…

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)The radius of a sphere decreases at the rate of 1 m/sec. Find the rate at which the volume…

Q: 2. The edge of a cube decreases at a rate of 1.5m/s. Find the rate at which the surface area…

A: Solution Calculate the area of cube

Q: 4. Water is running out of a conical tank 3 m across the top and 4 m deep at the rate of 2 m3 /min.…

A: given h = 4 m (Note: measurement of h is always taken from bottom) r = (3 ÷ 2 ) = 1.5 m dVdt = 2…

Q: 14. As sand leaks out of a hole in a container, it forms a conical pile whose altitude is always the…

A: We have to find the rate at which the sand is leaking out when the height is 10 in. Or we can say…

Q: 2) The radius of a sphere decreases at the rate of 4 m/sec. Find the rate at which the volume…

Q: 2)The radius of a sphere decreases at the rate of 1 m/secm/sec. Find the rate at which the volume…

Q: A bacterial cell is spherical in shape. If the radius of the cell is increasing at the rate of 0.01…

A: Volume of sphere: V = 43πr3, where r is radius of sphere. Surface area of sphere: S = 4πr2, where r…

Q: 18 Show that the volume V of a regular tetrahedron, all of whose side lengths are s, is V = s°V2…

A: Given that the volume of a tetrahedron is: 1442cm3 So, V=112s32 So, 112s32=1442⇒s3=123⇒s=12

Q: The radius of a sphere decreases at a rate of 4 m/s. when the radius is 7 m, then the rate at which…

Q: 1. The width of a rectangle is increasing at a rate of 2 cm/sec, while the length increases at 3…

A: I have stated the used formulas in the solution

Q: - Show that the volume V of a regular tetrahedron, all of whose side lengths are s, is V = 2 (all…

Q: 1. The radius of a sphere increases at a rate of 2 m/sec. The rate at which the volume increases…

A: This question is based on the application of derivative.

Question

5. [
| The radius of a sphere increases at the rate of 5 m/sec. Find the rate at which the
volume of a sphere increases when
the radius is 12 m.

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

$Chain Rule$

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.