The height of a circular cylinder is 50 in. and decreases at the rate of 4 in/sec, while the radius at the base is 20 in and increases at a rate of 1 in/sec. At what rate is the volume changing. a. 2571 b. 7512 c. 5721 d. 1257 (ILLUSTRATE SOLUTION)

The height of a circular cylinder is 50 in. and decreases at the rate of 4 in/sec, while the radius at the base is 20 in and increases at a rate of 1 in/sec. At what rate is the volume changing. a. 2571 b. 7512 c. 5721 d. 1257 (ILLUSTRATE SOLUTION)

Elementary Geometry for College Students

6th Edition

ISBN:9781285195698

Author:Daniel C. Alexander, Geralyn M. Koeberlein

Publisher:Daniel C. Alexander, Geralyn M. Koeberlein

Chapter9: Surfaces And Solids

Section9.3: Cylinders And Cones

Problem 3E

See similar textbooks

Related questions

Q: Given the area of a circle A=πr^2, find the rate of change of diameter d if dA/dt=3cm/min and the…

A: To find: The rate of change of the diameter d. Given: The rate of change of area is dAdt=3…

Q: Suppose that the radius of the hut is increased by 2.5%. Calculate the following: (i) Percentage…

Q: Consider a right circular cylinder open top tin can with volume 1000 cm?. Suppose Rand H are the…

A: Given: Right circular cylinder with open top has volume 1000 cm3. R is the radius of the…

Q: The volume of a spherical balloon changes with respect to the radius r. At what rate (in ft°/ft)…

Q: The side of a cube decreases at a rate of 8 m/sec. Find the rate at which the volume changes, when…

A: Given data: The side of a cube is decreases at the rate of 8 m/s. The objective is to find the rate…

Q: The density of Venus is similar to that of Earth. The mass of Venus is 4. and its diameter is 12,100…

A: For the given Mass = 4.9 X 1024 kg Diameter = 12100 km The density of venus is

Q: Water is pouring into the conical vessel 15 cm deep and having a radius of 3.75 cm across the top.…

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 sphere is expanding at the rate of 6 cm/sec. The formula for the volume of a sphere is: V = Tr. dr…

Q: The side of a cube increases at the rate of 6 m/sec. The rate at which the volume of the cube…

A: Given, The side of a cube increases at the rate of 6 m/sec. The side of the cube is 4 m is m³/sec.

Q: Two containers designed to hold water are side by side, both in the shape of a cylinder. Container A…

A: We have been given the 2 cylinders. First, we have been given cylinder A with a radius of 9 feet and…

Q: 3. A lead pipe 3 cm thick has inner diameter of 4 cm. Find number of cubic centimeters of lead in a…

Q: The side of a cube increases at the rate of 5 m/sec. The rate at which the volume of the cube…

A: let side of cube is x then rate at which side increase is 5 m/secie. dxdt=5 m/sec

Q: dv If the volume of the cube increases at the rate of 15 m / sec, then the value of is dt dv dV a) =…

A: Find the value value of rate of increase of volume of a cube

Q: The radius of a right circular cone increases at a rate of 1.8 in / s, while its height decreases at…

A: To find the rate of change of volume

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: A cylindrical can is to be made using a metal sheet. If the volume of the cylinder is 432π in3, then…

Q: The radius of a sphere is decreasing at a rate of 1/4 cm/s. At what rate is the volume decreasing if…

A: Volume of the sphere , V=43πr3

Q: Assuming a constant temperature, match the change in volume that a gas occupies to the change in the…

Q: 3. The radius of a sphere ball is measured at r = 25 cm. Estimate error in the volume and surface…

A: The radius of a sphere is measured at r = 25 cm. We have to estimate error in the volume and surface…

Q: At a sand and gravel plant, sand is falling off a conveyor and onto a conical pile at a rate of 12…

Q: If the radius r of a sphere is expanding at a rate of 15 cm/min, find the rate at which the volume…

A: We have given radius of a sphere is expanding at a rate of 15 cm/min. So drdt=15 cm/min As Volume of…

Q: 8. A snowball is melting at 10 cm3/sec, how fast is the diameter shrinking when the current di- 4…

A: Given, A snow ball is melting at 10cm3/sec.we have to find how fast is diameter shrinking when the…

Q: If the radius of a sphere increases at a rate of 0.5 m/sec, then the rate at which the volume of the…

A: Find the rate at which volume of a sphere increase s

Q: The volume of the sphere is increasing at the rate of 6 cm?/hr. At what rate is its surface area…

Q: The volume of a sphere is increasing at the rate of 6 cm3/hr. at what rate is its surface area…

Q: The side of a cube decreases at a rate of 7 m/sec. Find the rate at which the volume changes, when…

Q: If the radius of a sphere increases at a rate of 1.5 m/sec, then the rate at which the volume of the…

Q: The radius of a sphere decreases at a rate of 3 m/s. when the radius is 9 m, then the rate at which…

Q: If a snowball melts so that its surface area decreases at a rate of 2 cm2/min, find the rate at…

Q: 3. The radius of a sphere ball is measured at r= 25 cm. Estimate error in the volume and surface…

Q: Consider a right circular cylinder open top tin can with volume 1000 cm3. Suppose Rand H are the…

Q: The side of a cube decreases at a rate of 7 m/sec. Find the rate at which the volume changes, when…

A: Let the side of the cube be a m Then, given dadt=-7m/sec (- sign indicates side is decreasing) To…

Q: The tank shown below is full of water. Recall that the density of water is 1000 kg/m². Suppose that…

A: Base(top) to height relation where 0≤x≤3 and 0≤y≤3 x=y So the rate volume is, ΔV = 8xΔy ΔV = 8yΔy…

Q: A company wishes to manufacture a box with a volume of 40 cubic feet that is open on top and is…

A: To find the width of the box that can be produced using the minimum amount of material.

Q: The radius of a sphere increases at a rate of 6m/sec, then the rate at which the volume increases…

A: Let's find.

Q: The side of a cube increases at a rate of 10 m/sec. Find the rate at which the volume of the cube…

A: Use the formula for volume of cube and take its derivative than substitute the given values.

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: Given the area in the first quadrant by x^2 = 8y, the line x = 4 and the x axis. What is the volume…

Q: Which of these would be an appropriate unit to describe the rate at which the price increases as the…

A: According to the question given. We have, Explanation: ->The dependent variable in the question…

Q: The radius of a sphere is decreasing at a rate of 1/4 cm/s. At what rate is the volume decreasing if…

A: The radius of a sphere is decreasing at a rate of 14cm/s.The radius is 2cm.

Q: The diameter of a cone is 16 meters. If the height is 1.5 times its radius, what is the volume of…

A: Given: Diameter of a cone is 16m.height of the cone is 1.5 times its radius.

Q: A cylindrical tank is designed to have a radius of 5 m and a height of 7 , but that the radius and…

Q: A cylinder has a base radius of 6ft and a height of 18ft. What is its volume in cubic ft, to the…

A: Given thatBase radius r = 6 ft.height h = 18 ft.volume of the cylinder is given byV =…

Q: The side of a cube increases at a rate of 10 m/sec. Find the rate at which the volume of the cube…

A: Let the side of the cube be x meter at time t So, it is given that, dx/dt = 10 And, the volume of…

Q: The radius of a sphere decreases at a rate of 5 m/s. when the radius is 7 m, then the rate at which…

Q: The side of a cube increases at the rate of 10 m/sec. The rate at which the volume of the cube…

Question

The height of a circular cylinder is 50 in. and decreases at the rate of 4 in/sec, while the radius at the base is 20 in and increases at a rate of 1 in/sec. At what rate is the volume changing.

a. 2571 b. 7512

c. 5721 d. 1257

(ILLUSTRATE SOLUTION)

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

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

For Exercises 23 through 34, round the answers to 1 decimal place. 34. All dimensions in Figure 39-24 are in inches. Find the volume. Volume=(2a+c)bh6
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. Compute the height of a prism with a base area of 2.7 square feet and a volume of 4.86 cubic feet.
The gasoline tank on an automobile is box-shaped with dimensions of 24 in. by 20 in. by 9 in. If 1 ft3 corresponds to 7.5 gal of gasoline, What is the capacity of the automobiles fuel tank in gallons?
A coffee can is shaped like a cylinder with height 7 inches and radius 5 inches. Find (a) the surface area and (b) the volume of the can. Round to the nearest tenth.
a For the through in the shape of half-cylinder, find the volume of water it will hold Use 3.14 and disregard the thickness b If the trough is to be painted inside and out, find the number of square feet to be painted Use 3.14.
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 exercises. Where necessary, round the answers to 2 decimal places unless otherwise specified. Compute the volume of a prism with a height of 26.500 centimeters and base of 610.00 square centimeter.
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 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.