SOLUTION: You are building a poolside deck and need to know how many fifty-pound bags of quickset concrete to buy. There are eleven support piers(4x4 posts that are 6 ft tall). Each diameter

Question 334697: You are building a poolside deck and need to know how many fifty-pound bags of quickset concrete to buy. There are eleven support piers(4x4 posts that are 6 ft tall). Each diameter support post will partially be put in a hole dug to the required dimensions(6 inch diameter and 1 yard deep). The cement should fill the rest of the hole. Each bag of cement is equal to 1 cubic foot.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

You don't specify, but I presume that you mean to put the wooden post all the way into the bottom of the hole. (I wouldn't do it that way in real life, but if this is just a math exercise, who cares).

What you need to do is calculate the volume in cubic feet of a cylinder that is one-half a foot in diameter (one-quarter foot radius) and has a height of 3 feet. Then from that, subtract the volume of a rectangular solid that is one-third foot by one-third foot by 3 feet. Finally, multiply the difference by 11 and round UP. The result will be the number of sacks of quickset concrete to buy. You need to round up because you won't be able to find a building supply store that will sell you a fractional part of a sack of ready-mix.

The formula for the volume of a cylinder is

The formula for the volume of a rectangular solid is

By the way, where did you get the idea that a 50lb sack of ready-mix makes a whole cubic foot? Last I looked, a 60lb sack makes a half a cubic foot.

John

My calculator said it, I believe it, that settles it

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