Question 1

Given the formula $$A = 3 \pi g$$, solve for $$g in $$terms of $$A$$ and $$\pi.$$

Accepted Answer

$$g = \dfrac{A}{3\pi}$$

Question 2

If $$A = 3 \pi g$$ and $$A = 18$$, $$\pi = 3$$, what is the value of $$g$$?

Accepted Answer

$$g = 2$$

Question 3

A scientist uses the formula $$A = 3 \pi g to $$calculate the gravitational force $$g on a $$planet. If $$A is $$doubled, what happens to the value of $$g$$?

Accepted Answer

$$g is $$doubled

Question 4

Which of the following steps correctly isolates $$g in $$the equation $$A = 3 \pi g$$?

Accepted Answer

Divide both sides by $$3\pi$$

Question 5

If $$g = \dfrac{A}{3\pi}$$ and $$A = 12$$, $$\pi = 3.14$$, what is the approximate value of $$g ($$rounded to two decimal places)?

Accepted Answer

$$g \approx 1.27$$

Question 6

A physics student rearranges the formula $$A = 3 \pi g to $$solve for $$g. $$Which of the following is the correct rearrangement?

Accepted Answer

$$g = \dfrac{A}{3\pi}$$

Question 7

In a chemistry experiment, the area $$A of a $$circular plate is given by $$A = 3 \pi g$$, where $$g is a $$scaling factor. If the area is measured as $$A = 9\pi$$, what is the value of $$g$$?

Accepted Answer

$$g = 3$$

Question 8

Which of the following real-world scenarios could be modeled by the formula $$A = 3 \pi g$$?

Accepted Answer

The area of three identical circular plates, each with area $$\pi g$$

Question 9

If $$A = 3 \pi g$$ and $$g is $$increased by a factor of 4, by what factor does $$A$$ increase?

Accepted Answer

It increases by a factor of 4

Question 10

A student incorrectly solves $$A = 3 \pi g$$ for $$g$$ and gets $$g = \dfrac{3\pi}{A}. $$What mistake did the student make?

Accepted Answer

They multiplied both sides by $$3\pi$$ instead of dividing

Question 11

If $$A = 3 \pi g$$ and $$A = 0$$, what is the value of $$g$$?

Accepted Answer

$$g = 0$$

Question 12

Which of the following best describes the relationship between $$A$$ and $$g in $$the formula $$A = 3 \pi g$$?

Accepted Answer

$$A is $$directly proportional to $$g$$

Solving for a Variable in a Formula: Isolating g in A = 3πg

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