Activity 3.1.2 Calculating Needs



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[pic]Activity 3.1.2 – Calculating Needs

Purpose

If you were asked to order potting media to plant 2000 geraniums for the spring plant sale, how would you know how much to get? With so many little pots to fill how could you determine a bulk quantity of media needed?

This is an example of a practical situation that producers of container-grown crops face. You could guess an amount and have a truckload of media delivered, but what do you do with the left over mix? The best estimates are based on mathematics to determine the quantity that will be used. It is not too difficult to make reasonable estimates with a little practice.

Potting media is typically sold by the cubic yard because it is very bulky. A cubic yard of media would fill up a 3′ deep by 3′ wide by 3′ tall cardboard box. However, in many cases, the containers that plants are grown in are round or irregular shaped. The challenge is to order enough media required for all of the plants, but not have a pile of extra left over.

Materials

|Per student: | |

|Calculator | |

|Pencil | |

|Agriscience Notebook | |

Procedure

Calculate the volume of potting media you will need in order to fill the containers that are discussed in the problems presented in this activity. Use the example problems to help you understand how to solve each practice problem. Once completed, use this knowledge to determine the potting media order for a local greenhouse in Part 2.

Part 1 – Practice Situations

Example Problem #1:

Cory decided to add sand to his flowerbeds to improve drainage. He ordered two cubic yards of sand and it was dumped in his driveway. To move the sand to his flowerbeds he decided to use plastic buckets. Cory calculated how many full buckets of sand he would have to move and was surprised.

He figured out the mathematical problem presented in this situation was a volume calculation. Therefore, to solve it he needed to measure the size of the bucket to determine its volume. Once he knew the volume of the bucket, he could figure how many buckets it would take to move the pile of sand, since he already knew the pile contained two cubic yards.

Plastic bucket = 12″ tall x 12″ diameter

Cory remembered that the formula for the area of a cylinder is pi x radius2 x length. From his experience in mathematics class, he decides this is the correct formula needed to determine the volume of his bucket. The only issues he must keep in mind are:

• pi equals 3.14.

• Length of the bucket, in this case length is considered the height of the bucket.

• Radius is half of the diameter of the bucket.

• Units need to be consistent, while using the formula – he can convert his answer later to the units he needs to finish the problem.

|Bucket volume = |3.14 x (6)2 x 12 = |

| |3.14 x 36 x 12 = |

| |1356.48 cubic inches |

Now this is great, but the volume of the bucket is in cubic inches and that does not help Cory when the sand is measured in cubic yards. He must convert:

• There are 1728 cubic inches in one cubic foot

• There are 27 cubic feet in one cubic yard

|1728 in3 |x |27 ft3 |= |x in3 |

|1 ft3 | |1 yd3 | |1 yd3 |

|1728 in3 |x |27 ft3 |= |46,656 in3 |

|1 ft3 | |1 yd3 | |1 yd3 |

This means that there are 46,656 cubic inches per cubic yard. Cory has two cubic yards of sand to move or 69 bucketfuls. That is a lot of buckets to move!

|How many bucketfuls: |46,656 in3 x 2 yd3 = 93,312 in3 |

| |93,312 in3 / 1356.48 in3 = 68.8 buckets |

Now you try a couple problems related to a greenhouse situation:

|Table 1 Practice Problems |

|Type of Container |Measurements |Volume |

|6″ Azalea Pot |6″ diameter by 6″ tall |in3 |

|Hanging Basket |16″ diameter by 10″ tall |in3 |

|Patio Planter |24″ diameter by 18″ tall |ft3 |

|Show work: |

| |

Example Problem #2:

Samantha decided to refresh her bark mulch around the house. She did not know exactly how much bark she needed, but she remembered from a few years prior that she made several pickup trips back and forth from the landscape supply store hauling bark. Since the price of bark increased to $32.00 per cubic yard, she decided only to get 3 cubic yards total this time. Now, Samantha wants to calculate how many pickup loads are needed to haul the bark mulch.

What Samantha is determining is the area of a three-dimensional rectangular object since this is the shape of a pickup bed. She knows the volume of a square-shaped or rectangular-shaped object is Length x Width x Height. Samantha will be able to determine how much her pickup will carry each trip using this information.

The pickup truck bed is rectangular and has dimensions of 8′ long, 5′ wide, and 2′ deep.

|Therefore, | |

|The volume of the pickup bed = |8′x 5′ x 2′ = 80 ft3 |

Now that Samantha knows the carrying capacity of her pickup in cubic feet, she is able to determine the capacity in cubic yards with a simple proportion problem:

|27 ft3 |= |80 ft3 |

|1 yd3 | |x yd3 |

|Cross multiply: |27x = 80 | | | |

|Divide each side by 27 to solve for “x” |27x |= |80 | |

| |27 | |27 | |

|Answer: |x |= |2.9 yd3 | |

Samantha can get all of the bark mulch in one trip.

Now you try a couple problems related to a greenhouse situation:

|Table 2 Practice Problems |

|Type of Container |Measurements |Volume |

|4″ Square Pot |4″ x 4″ x 4″ |in3 |

|Windowsill Box |16″ x 6″ x 6″ |ft3 |

|Soil Sterilizer |3′ x 2′ x 2′ |yd3 |

|Show work: |

| |

Part 2 – Potting Media Order

You have applied for a job at the local greenhouse operation. During the job interview, the owner asks you to make the decision regarding the purchase of potting media for this year’s spring crops. Two suppliers have provided bids, and you need to determine how much media is needed and determine the supplier that can provide the best price.

|Table 3 Meadow Grove Greenhouses’ Planting Schedule |

|Crop |Quantity |Container Size |Cubic Yards of Media Needed |

|Dahlia |450 |6″ x 6″ x 8″ square |yd3 |

|Show work: |

|Trailing Petunia |600 |4″ x 4″ x 4″ square |yd3 |

|Show work: |

|Browallia |300 |4″ x 4″ round |yd3 |

|Show work: |

|Impatiens Baskets |525 |1′ diameter x 8″ tall |yd3 |

|Show work: |

|Vegetable Starts |875 |2″ x 2″ x 3″ square |yd3 |

|Show work: |

|Marigold 6-Packs |400 |1.5″ x 2″ x 3″ cells |yd3 |

| | |(6 per container) | |

|Show work: |

|Estimated Cubic Yards of Media Required: |yd3 |

Using the following information provided from the suppliers, determine the total cost of media for both options. The owner needs this information to make his decision since Gustafson Horticultural Supply is a further distance away from the greenhouses than Valley Greenhouse Company.

|Media Supplier: |Product Packaging |Cost |

|Gustafson Horticultural Supplies |7 ft3 Bale |$14.75/bale |

|Valley Greenhouse Company |Bulk |$62.00/yd3 |

|Table 4 Price Comparison |

|Show work related to solving the cost comparison problems: |

|Gustafson Horticultural Supplies |Valley Greenhouse Company |

| | |

|Gustafson’s Total Cost: |$ |Valley’s Total Cost: |$ |

Conclusion

1. What is important when calculating area using different units of measurements?

2. List the steps you would use to convert cubic feet into cubic yards.

3. Why is it important to compare product costs on the same unit size?[pic][pic]

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