You want to put a 2 inch thick layer of topsoil for a new 27 ft by 32 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.

First, let's determine the volume of the layer of topsoil. That would be equal to the product of the dimensions of the garden, times the height of the layer of soil. To maintain consistency of units, 2 inches is equal to 1/6 ft

Volume = (27 ft)(32 ft)(1/6 ft) = 144 ft³

Also, 1 yard is equal to 3 feet. So, the equivalent volume in cubic yards is

Volume = 144 ft³ (1 yard/3 ft)³ = 16/3 yd³
Amount of cubic yards = 16/3 yd³/1/4 yd³ = 21 1/3 

Thus, you would need to buy 21 and 1/3 of 1/4 cubic yards so that it will have a total volume of 16/3 or 5.33 cubic yards.

Geometric pattern of 2 i’m guessing. not really sure about what you’re asking but i hope this !