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f=3pi((d)/(2))^(2)h
A board foot is a 1 foot by 1 foot by 1 inch thick volume. The formula estimates the board feet,
f, available in a tree with a diameter of
d inches and a height of
h feet. Which of the following equations correctly gives the diameter in terms of the board feet and the height of the tree?
Choose 1 answer:
(A)
d=sqrt((2f)/(3pi h))
(B)
d=2sqrt((f)/(3pi h))
(C)
d=(2f^(2))/(3pi h)
(D)
d=(f^(2)sqrt2)/(3pi h)

$f=3 \pi\left(\frac{d}{2}\right)^{2} h$ $\newline$ A board foot is a $1$ foot by $1$ foot by $1$ inch thick volume. The formula estimates the board feet, $f$ , available in a tree with a diameter of $d$ inches and a height of $h$ feet. Which of the following equations correctly gives the diameter in terms of the board feet and the height of the tree? $\newline$ Choose $1$ answer: $\newline$ (A) $d=\sqrt{\frac{2 f}{3 \pi h}}$ $\newline$ (B) $d=2 \sqrt{\frac{f}{3 \pi h}}$ $\newline$ (C) $d=\frac{2 f^{2}}{3 \pi h}$ $\newline$ (D) $d=\frac{f^{2} \sqrt{2}}{3 \pi h}$

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Volume of cubes and rectangular prisms: word problems

Full solution

Q.

f=3 \pi\left(\frac{d}{2}\right)^{2} h

\newline

A board foot is a

1

foot by

1

foot by

1

inch thick volume. The formula estimates the board feet,

f

, available in a tree with a diameter of

d

inches and a height of

h

feet. Which of the following equations correctly gives the diameter in terms of the board feet and the height of the tree?

\newline

Choose

1

answer:

\newline

(A)

d=\sqrt{\frac{2 f}{3 \pi h}}

\newline

(B)

d=2 \sqrt{\frac{f}{3 \pi h}}

\newline

(C)

d=\frac{2 f^{2}}{3 \pi h}

\newline

(D)

d=\frac{f^{2} \sqrt{2}}{3 \pi h}

Isolate $(\frac{d}{2})^2$ : We have the original formula: $f = 3\pi\left(\left(\frac{d}{2}\right)^2\right)h$ . We need to solve for $d$ .
Solve for $d/2$ : First, divide both sides by $3\pi h$ to isolate $(d/2)^2$ on one side: $(d/2)^2 = \frac{f}{3\pi h}$ .
Solve for d: Next, take the square root of both sides to solve for $d/2$ : $d/2 = \sqrt{f/(3\pi h)}$ .
Solve for d: Next, take the square root of both sides to solve for $d/2$ : $d/2 = \sqrt{f/(3\pi h)}$ . Finally, multiply both sides by $2$ to solve for d: $d = 2\sqrt{f/(3\pi h)}$ .

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