Answered: All edges of a cube are expanding at a…

All edges of a cube are expanding at a rate of 8 mm per hour. At what rate is the volume of the cube changing when each edge is 16 mm?

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter9: Surfaces And Solids

Section9.1: Prisms, Area And Volume

Problem 33E: When the length of each edge of a cube is increased by 1 cm, the volume is increase by 61 cm3. What...

See similar textbooks

Related questions

Q: All edges of a cube are expanding at a rate of 8 centimeters per second. (a) How fast is the surface…

A: Surface area of cube = 6x2Where x is the edge of the cube

Q: Suppose the edges of a cube are increasing at a constant rate of 8 m/hr. Then, the volume of the…

Q: Suppose that the sides of a cube are expanding at a rate of 2 inches per minute. How fast i the…

A: We need to find the rate of change of volume of cube when side is 20 inches. Volume of cube=(side)3…

Q: The edges of a cube are expanding at a rate of 5cm per second. How fast is the volume changing when…

Q: All edges of a cube are expanding at a rate of 9 centimeters per second. (a) How fast is the volume…

A: GivenAll edges of a cube are expanding at a rate of 9 centimeters per second

Q: All edges of a cube are expanding at a rate of 3 cm per second. How fast is the volume changing when…

Q: All edges of a cube are expanding at a rate of 8 centimeters per second. (a) How fast is the volume…

Q: All edges of a cube are expanding at a rate of 6 centimeters per minute. Draw an accurate picture…

Q: A rectangular parallelepiped with an altitude of 10cm has its width decreasing by 2 cm/min and…

A: A rectangular parallelepiped with an altitude of 10cm has its width decreasing by 2 cm/min and…

Q: All edges of a cube are expanding at a rate of 8 centimeters per second. (a) How fast is the volume…

Q: The volume of a cube is decreasing at a rate of 24 cubic inches per minute. At the instant when an…

A: Given that The volume of a cube is decreasing at a rate of 24 cubic inches per minute.…

Q: All edges of a cube are expanding at a rate of 2 centimeters per second. (a) How fast is the surface…

A: We have given change in edge with respect to time is 2cm/sec. We have to find the changes in…

Q: All edges of a cube are expanding at a rate of 3 centimeters per second. (a) How fast is the surface…

Q: A cube has sides that are increasing at a rate of 10 cm/s. At what rate is the volume increasing…

A: Valur=?

Q: Suppose the sides of a cube are expanding at a rate of 2 inches per minute, How fast is the volume…

Q: A force is applied to a particle, which moves in a straight line, in such a way that after each…

A: A geometric series is convergent if common ratio is less than 1. Sum of infinite geometric series is…

Q: The volume of a cube is increasing at the rate of 21 cc/min. At what rate is its surface area…

A: The volume of a cube is increasing at rate, dVdt = 21 cc/min To evaluate: The rate at which the…

Q: the

Q: All edges of a cube are expanding at a rate of 8 centimeters per second. How fast is the volume…

A: All edges of a cube are expanding at a rate of 8 centimeters per second. Let the edge of a cube = x…

Q: The sides of an equilateral triangle are increasing at a rate of 10 cm/min. At what rate is the area…

A: let side of triangle = x Given

Q: A sphere is filled with air. If the volume of the sphere is decreasing at a rate of 534 cubic cm per…

A: Given

Q: All edges of a cube are expanding at a rate of 6 cm per second. How fast is the volume changing when…

Q: 1000 liters of water per second is filled into the square prism-shaped tank with a base edge of 10…

A: We have to find the relating equation of volume with height and then differentiate it with respect…

Q: The original 24 m edge length of a cube decreases at the rate of 2 m divided by two minutes When x=1…

Q: The original 24 m edge length x of a cube decreases at the rate of 5 m/min. a. When x=5m, at what…

Q: If the volume of a cube is increasing at a rate of 24 in'/min and each edge is increasing at 2…

A: The volume of cube is given by V=a3 where a edge of cube. Given that volume of cube increasing at a…

Q: All edges of a cube are expanding at a rate of 3 centimeters per second. (a) How fast is the volume…

Q: All edges of a cube are expanding at a rate of 6 centimeters per second. How fast is the volume…

A: It is given that dsdt=6 cms. It is known that V=s3. Differentiate the above equation with respect to…

Q: All edges of a cube are expanding at a rate of 2 centimeters per second. (a) How fast is the surface…

A: we know that surface area of cube is , S = 6 • a 2 Here a is side of cube .

Q: The radius of a right circular cone is increasing at a rate of 5 inches per second and its height is…

Q: All the edges of a cube are expanding at a rate of 6 centimeters per second. How fast is the volume…

Q: If the radius of a sphere is increasing at the constant rate of 3 inches per second, how fast is the…

A: Given dr/dt = 3

Q: All edges of a cube are expanding at a rate of 7 cm per second. How fast is the surface area…

A: Given that all edges of a cube are expanding at a rate of 7 cm per second. Let the edge of a sphere…

Q: If the first swing of this pendulum travels for 42 cm and its successive swing decreases by 20%,…

A: The distance travelled by the pendulum in the first swing is d1=42 cm. The distance travelled in the…

Q: All edges of a cube are expanding at a rate of 8 centimeters per second. How fast is the surface…

A: Since, we have been given that all edges of a cube are expandingat a rate of 8 centimeters per…

Q: How fast is the volume of a cube changing when the edge is 15 cm if the edge is changing at the rate…

Q: All edges of a cube are expanding at a rate of 9 centimeters per second. How fast is the volume…

Q: The radius of a sphere is increasing at a rate of 4 meters per minute. When the radius is 11 meters,…

Q: as a balloon in the shape of a sphere is being blown up, the volume is increasing at the rate of 4…

A: Volume of the sphere Shape ballon: V = 4/3ℼr3 (r = radius) Now differentiate with respect to L,…

Q: All edges of a cube are expanding at a rate of 9 centimeters per second. How fast is the volume…

A: Explanation of the answer is as follows

Q: The side of a cube is increasing at a rate 9m/s, then the rate at which the volume of the cube…

A: The function f(t) is a rule that associates or fixes a number to the particular point t. The…

Q: 2. All edges of a cube are expanding at a rate of 6 centimeters per second. How fast is the volume…

Q: A toxic radioactive substance with a density of 9 milligrams per square cm is detected in the…

A: It is given that, A toxic radioactive substance with a density of 9 milligrams per square cm is…

Q: All edges of a cube are expanding at a raete of 6 centimeters per second. How fast is the surface…

Q: The radius of a right circular cone is increasing at a rate of 3 inches per second and its height is…

Q: If the original 24 m edge length x of a cube decreases at the rate of5 m/min, when x = 3 m at what…

A: If the original 24 m edge length x of a cube decreases at the rate of5 m/min, when x = 3 m at what…

Q: A tank is shaped like an upside-down square pyramid, with a base with sides that are 4 meters in…

Q: All edges of a cube are expanding at a rate of 6 centimeters per second. How fast is the volume…

A: Given that, All edges of a cube are expanding at a rate of 6 centimeters per second. Thus, dxdt=6…

Concept explainers

Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.

Question

Please show your work

3. All edges of a cube are expanding at a rate of 8 mm per hour. At what rate is the volume of the cube
changing when each edge is 16 mm?
F7
esc
F1
23
2$
&
4
5
6.
8
9
7.
2
Y
Q
W
K
S
D
F
T

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 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Matrix Operations$

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

The numerical value of the volume of a cube equals the numerical value of its total surface area. What is the length of each edge of the cube?
As in Exercise 39, find the volume of the box if four congruent squares with sides of length 6 in. are cut from the corners of a rectangular piece of poster board that is 20 in. wide by 30 in. long. Kristine creates an open box by cutting congruent squares from the four corners of a square piece of cardboard that has a length of 24 in. per side. If the congruent squares that are removed have sides that measure 6 in. each, what is the volume of the box formed by folding and sealing the flaps?
For a right circular cone, the dimensions are r=6 cm and h=8 cm. If the length of the radius is doubled while the height is made half as large in forming a new cone, will the volumes of the two cones be equal?
Kristine creates an open box by cutting congruent squares from the four corners of a square piece of cardboard that has a length of 24 in. per side. If the congruent squares that are removed have sides that measure 6 in. each, what is the volume of the box formed by folding and sealing the flaps?
The tin can shown at the right has the indicated dimensions. Estimate the number of square inches of tin required for its construction. HINT: Include the lid and the base in the result.
The surface of a soccer ball is composed of 12 regular pentagons and 20 regular hexagons. With each side of each regular polygon measuring 4.5 cm, the area of each regular pentagon is 34.9 cm2 and area of each regular hexagon is 52.5 cm2. a What is the surface area of the soccer ball? b If the material used to construct the ball costs 0.8 of a cent per square centimeter, what is the cost of the materials used in construction?
When the length of each edge of a cube is increased by 1 cm, the volume is increase by 61 cm3. What is the length of each edge of the original cube?
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?