I have a question about Problem solving from a college course called Quantitative Reasoning

Question

You want to put a 4-inch thick layer of topsoil for a new 12 ft by 29 ft garden. The dirt store sells by the cubic yards. How many cubic yards will you need to order? The store only sells in increments of 1/4 cubic yards.

Answer 1

Hi Abigail!

This type of problem can feel tricky because in addition to the calculation itself, you're also expected to convert units.

I find it easiest to see what units the answer requires, and convert everything to that unit from the very beginning. This is especially true for area and volume questions, where it's easy to lose track of the conversion for squared or cubed units.

So, for this question, I would first convert my "givens" to yards:

4 inches = 1/3 feet = 1/9 yards

12 feet = 4 yards

29 feet = 9 2/3 yards

Now it's a fairly simple volume question, in which you multiply the height, length, and width:

(1/9) * (4) * (9+2/3) = 4.296 cubic yards

Rounding up to the nearest 1/4 cubic yard, you get 4.5 cubic yards.

I hope that helps!

Katherine

P.S. When converting units from the beginning, be careful not to round until the very end.

Answer 2

1 cubic yard = 1 yd x 1 yd x 1 yd = 36 in x 36 in x 36 in = 46656 cubic inches

Volume needed = 12 ft x 29 ft x 4 inches = (12 x 12) x (29 x 12) x 4 cubic inches = 200 448 cubic inches

200448 / 46656 = 4.296 cubic yards needed

We have to round up to the next 1/4 cubic yard. (so to the first of 4.5, 4.75, 5.00 ...) .

This will be 4.5, so you need to order 4.5 cubic yards