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related rates

related rates

Assessment

Flashcard

Mathematics

11th - 12th Grade

Practice Problem

Hard

Created by

Wayground Content

FREE Resource

Student preview

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15 questions

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1.

FLASHCARD QUESTION

Front

What is related rates in calculus?

Back

Related rates involve finding the rate at which one quantity changes with respect to another, using derivatives and the chain rule.

2.

FLASHCARD QUESTION

Front

What is the formula for the area of a circle?

Back

A = πr², where A is the area and r is the radius.

3.

FLASHCARD QUESTION

Front

How do you find the rate of change of the area of a circle with respect to time?

Back

Use the formula dA/dt = 2πr(dr/dt), where dr/dt is the rate of change of the radius.

4.

FLASHCARD QUESTION

Front

What is the volume formula for a sphere?

Back

V = (4/3)πr³, where V is the volume and r is the radius.

5.

FLASHCARD QUESTION

Front

How do you find the rate of change of the volume of a sphere with respect to time?

Back

Use the formula dV/dt = 4πr²(dr/dt).

6.

FLASHCARD QUESTION

Front

If the radius of a circle is increasing at a constant rate, how does that affect the area?

Back

The area increases at a rate proportional to the square of the radius.

7.

FLASHCARD QUESTION

Front

What is the relationship between the radius and the area of a circle?

Back

The area of a circle is directly proportional to the square of its radius.

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