What is the total volume of a planter that has a 6x6 opening

Question

An architect is designing flower planters for apark. Each planter consists of a border of 1-foot concrete cubes surrounding a square opening. Each concrete cube weighs 120 pounds. The diagram below shows the top view of some of the planters.

Answer 1

Hi Eileen,

 

Your question looks a little incomplete, but let's have a go at it.

 

The blocks surrounding the planter are 1 foot cubes, which means they measure (1 ft x 1 ft x 1 ft) and each have a volume of 1 cubic ft. (volume = length x height x width).  The blocks surround a 6 ft x 6 ft opening.  Which means that the volume inside the planter measures 6 ft x 6 ft x 1 ft . The volume of the space inside the planter is then 6 x 6 x 1 = 36 cubic ft.  It will take 6 blocks per side + 4 corner blocks to build the planter.  There are four sides.  The number of blocks is (4 x 6) + 4 = 28.  Since each block is 1 cubic ft, The volume of the concrete blocks is 28 cubic ft.  The volume of the blocks and the space inside combined is just the sum 28 + 36 = 64 cubic ft.

 

Alternatively, you can arrive at the same answer by counting the blocks along each side (8) and multiplying 8 x 8 x 1 = 64.