Question

the total weight of a rock depends on its size and is proportional to its density. in this context, density is the weight per cubic inch. let w denote the weight of the rock in pounds, s the size of the rock in cubic inches, and d the density of the rock in pounds per cubic inch.
(a) what is the total weight of a 9 - cubic - inch rock that weighs 2 pounds per cubic inch?
(b) write an equation that shows the proportionality relation.
(c) use the equation you found in part (b) to find the total weight of a 11 - cubic - inch rock with density 0.3 pound per cubic inch.

Explanation:

Step1: Recall weight - density - size relation

The weight $w$ of a rock is given by the formula $w = s\times d$, where $s$ is the size and $d$ is the density.

Step2: Solve part (a)

Given $s = 9$ cubic - inches and $d=2$ pounds per cubic - inch. Substitute into the formula $w=s\times d$. So $w = 9\times2=18$ pounds.

Step3: Analyze proportionality equation

The proportionality relation between weight $w$, size $s$, and density $d$ is $w = s\times d$. Here, the size $s$ is the constant of proportionality when considering $w$ and $d$ (since $w$ is directly proportional to $d$ with $s$ held constant).

Step4: Solve part (c)

Given $s = 11$ cubic - inches and $d = 0.3$ pounds per cubic - inch. Substitute into the formula $w=s\times d$. So $w=11\times0.3 = 3.3$ pounds.

Answer:

(a) 18
(b) $w = s\times d$
(c) 3.3