Question

linda built a compost bin in the shape of a rectangular prism. the bin is 48 in long, 24 in wide, and 48 in deep. after the compost cycle is complete, the bin will be full of potting soil that linda can sell at a farmer’s market. the potting soil will be packaged in bags. the amount of soil each bag can hold is known in cubic feet.
(a) find the volume of the compost bin in cubic feet. use the table of conversion facts, as needed.
(b) linda is going to put the potting soil in bags. each bag holds 0.55 ft³ of the soil. she is going to bag up as much soil as possible, but she won’t partially fill any bags. how many whole bags will she fill?
(c) the bags will sell for $4.99 each. if linda sells all the bags, how much money will she collect?
conversion facts for length
1 foot (ft) = 12 inches (in)
1 yard (yd) = 3 feet (ft)
1 yard (yd) = 36 inches (in)

Explanation:

Part (a)

Step1: Convert inches to feet

We know that \( 1 \) foot \( = 12 \) inches. So, for length: \( 48 \) inches \(=\frac{48}{12}=4\) feet, width: \( 24 \) inches \(=\frac{24}{12} = 2\) feet, depth: \( 48 \) inches \(=\frac{48}{12}=4\) feet.

Step2: Calculate volume of rectangular prism

The formula for the volume \( V \) of a rectangular prism is \( V=l\times w\times h \), where \( l \) is length, \( w \) is width and \( h \) is height (depth here). Substituting \( l = 4\), \( w=2\), \( h = 4\) into the formula, we get \( V=4\times2\times4\).

Step3: Compute the volume

\( 4\times2\times4 = 32\) cubic feet.

Step1: Divide total volume by volume per bag

We know the total volume of soil is \( 32\) cubic feet (from part a) and each bag holds \( 0.55\) cubic feet. So, the number of bags \( n=\frac{32}{0.55}\).

Step2: Calculate the number of whole bags

\( \frac{32}{0.55}\approx58.18\). Since we need whole bags, we take the floor value, so \( n = 58\).

Step1: Multiply number of bags by price per bag

We know the number of bags is \( 58\) (from part b) and each bag is sold for \( \$4.99\). So, total money \( M=58\times4.99\).

Step2: Compute the total money

\( 58\times4.99=58\times(5 - 0.01)=58\times5-58\times0.01 = 290- 0.58=\$289.42\)

Answer:

The volume of the compost bin is \( \boldsymbol{32}\) cubic feet.

Part (b)