Deshaun built a compost bin in the shape of a rectangular prism. The bin is
4ft
long,
2ft
wide, and
4ft
deep. After the compost cycle is complete, the bin will be full of potting soil that Deshaun 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 inches.
(a) Find the volume of the compost bin in cubic inches. Use the table of conversion facts, as needed.
in3
(b) Deshaun is going to put the potting soil in bags. Each bag holds
415in3
of the soil. He is going to bag up as much soil as possible, but he won't partially fill any bags. How many whole bags will he fill?
bags
(c) The bags will sell for
$4.99
each. If Deshaun sells all the bags, how much money will he collect?
$
(a) To find the volume of the compost bin in cubic inches, we need to convert the measurements to inches and then multiply them together:
4ft = 48in (since there are 12 inches in a foot)
2ft = 24in
4ft = 48in
Volume = length x width x height
Volume = 48in x 24in x 48in
Volume = 55,296in3
Therefore, the volume of the compost bin is 55,296 cubic inches.
(b) Each bag holds 415 cubic inches of soil. To find out how many whole bags can be filled, we divide the volume of the compost bin by the volume of each bag:
Number of bags = Volume of compost bin ÷ Volume of each bag
Number of bags = 55,296in3 ÷ 415in3
Number of bags ≈ 133.12
Since we can't have a fraction of a bag, Deshaun will be able to fill 133 whole bags with potting soil.
(c) Each bag sells for $4.99, and Deshaun is able to fill 133 bags. To find out how much money he will make, we multiply the number of bags by the price per bag:
Total earnings = Number of bags x Price per bag
Total earnings = 133 x $4.99
Total earnings = $664.67
Therefore, if Deshaun sells all the bags, he will collect $664.67.
(a) To find the volume of the compost bin in cubic inches, we need to multiply its length, width, and depth:
Volume = length x width x depth
= 4ft x 2ft x 4ft
Since we need the volume in cubic inches, we have to convert the measurements to inches. We know that 1 ft is equal to 12 inches.
So, the volume of the compost bin in cubic inches = 48in x 24in x 48in.
Calculating this, we get:
Volume = 55,296 cubic inches.
(b) To find out how many whole bags can be filled, we need to divide the volume of the compost bin by the volume of each bag:
Number of bags = Volume of compost bin / Volume of each bag
= 55,296 / 415
Calculating this, we get:
Number of bags ≈ 133.44
Since Deshaun cannot have partial bags, he can only fill whole bags. So, he can fill 133 whole bags.
(c) To calculate how much money Deshaun will collect, we need to multiply the number of bags filled by the price per bag:
Total money collected = Number of bags x Price per bag
= 133 x $4.99
Calculating this, we get:
Total money collected ≈ $663.67