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Example Questions
Example Question #3431 : Calculus
A regular tetrahedron is burgeoning in size. What is the ratio of the rate of change of the surface area of the tetrahedron to the rate of change of its height when its sides have length ?
To solve this problem, define a regular tetrahedron's dimensions, its surface area and height, in terms of the length of its sides:
Rates of change can then be found by taking the derivative of each property with respect to time:
The rate of change of the sides isn't going to vary no matter what dimension of the tetrahedron we're considering; is . Find the ratio by dividing quantities:
Example Question #608 : Rate
A regular tetrahedron is decreasing in size. What is the ratio of the rate of change of the surface area of the tetrahedron to the rate of change of its height when its sides have length 55?
To solve this problem, define a regular tetrahedron's dimensions, its surface area and height, in terms of the length of its sides:
Rates of change can then be found by taking the derivative of each property with respect to time:
The rate of change of the sides isn't going to vary no matter what dimension of the tetrahedron we're considering; is . Find the ratio by dividing quantities:
Example Question #609 : Rate
A regular tetrahedron is decreasing in size. What is the ratio of the rate of change of the surface area of the tetrahedron to the rate of change of its height when its sides have length ?
To solve this problem, define a regular tetrahedron's dimensions, its surface area and height, in terms of the length of its sides:
Rates of change can then be found by taking the derivative of each property with respect to time:
The rate of change of the sides isn't going to vary no matter what dimension of the tetrahedron we're considering; is . Find the ratio by dividing quantities:
Example Question #521 : How To Find Rate Of Change
A regular tetrahedron is decreasing in size. What is the ratio of the rate of change of the surface area of the tetrahedron to the rate of change of its height when its sides have length 30?
To solve this problem, define a regular tetrahedron's dimensions, its surface area and height, in terms of the length of its sides:
Rates of change can then be found by taking the derivative of each property with respect to time:
The rate of change of the sides isn't going to vary no matter what dimension of the tetrahedron we're considering; is . Find the ratio by dividing quantities:
Example Question #522 : How To Find Rate Of Change
A regular tetrahedron is decreasing in size. What is the ratio of the rate of change of the surface area of the tetrahedron to the rate of change of its height when its sides have length ?
To solve this problem, define a regular tetrahedron's dimensions, its surface area and height, in terms of the length of its sides:
Rates of change can then be found by taking the derivative of each property with respect to time:
The rate of change of the sides isn't going to vary no matter what dimension of the tetrahedron we're considering; is . Find the ratio by dividing quantities:
Example Question #523 : How To Find Rate Of Change
A regular tetrahedron is decreasing in size. What is the ratio of the rate of change of the surface area of the tetrahedron to the rate of change of its height when its sides have length ?
To solve this problem, define a regular tetrahedron's dimensions, its surface area and height, in terms of the length of its sides:
Rates of change can then be found by taking the derivative of each property with respect to time:
The rate of change of the sides isn't going to vary no matter what dimension of the tetrahedron we're considering; is . Find the ratio by dividing quantities:
Example Question #3437 : Calculus
A regular tetrahedron is decreasing in size. What is the ratio of the rate of change of the surface area of the tetrahedron to the rate of change of its height when its sides have length ?
To solve this problem, define a regular tetrahedron's dimensions, its surface area and height, in terms of the length of its sides:
Rates of change can then be found by taking the derivative of each property with respect to time:
The rate of change of the sides isn't going to vary no matter what dimension of the tetrahedron we're considering; is . Find the ratio by dividing quantities:
Example Question #3438 : Calculus
A cube is growing in size. What is the ratio of the rate of growth of the cube's volume to the rate of growth of its surface area when its sides have length 200?
Begin by writing the equations for a cube's dimensions. Namely its volume and surface area in terms of the length of its sides:
The rates of change of these can be found by taking the derivative of each side of the equations with respect to time:
Now, knowing the length of the sides, simply divide to find the ratio between the rate of change of the volume and surface area:
Example Question #524 : How To Find Rate Of Change
A cube is growing in size. What is the ratio of the rate of growth of the cube's volume to the rate of growth of its surface area when its sides have length 164?
Begin by writing the equations for a cube's dimensions. Namely its volume and surface area in terms of the length of its sides:
The rates of change of these can be found by taking the derivative of each side of the equations with respect to time:
Now, knowing the length of the sides, simply divide to find the ratio between the rate of change of the volume and surface area:
Example Question #3431 : Calculus
A cube is growing in size. What is the ratio of the rate of growth of the cube's volume to the rate of growth of its surface area when its sides have length 316?
Begin by writing the equations for a cube's dimensions. Namely its volume and surface area in terms of the length of its sides:
The rates of change of these can be found by taking the derivative of each side of the equations with respect to time:
Now, knowing the length of the sides, simply divide to find the ratio between the rate of change of the volume and surface area:
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