Geometry Word Problem

Question

Landscaping rock is sold in bags that contain 0.5 cubic feet of rocks. Mark wants to cover his flower garden with a 2 inch thick layer of river stone. His flower bed is 4 feet wide and 18 feet long. Mark has 10 bags of river stone in his garage. To the nearest whole bag, how many more bags will he need to cover his flower garden?

 

A. 14

B. 26

C. 62

D. 134

Answer 1

Hello Chandler,

 

This is a simple Volume problem.

First lets find out how much volume we have to fill.

 

Recall that

 

Volume for a rectangle is

 

Volume = Length x Width x Height

 

such that,

 

V = LWH = (18 ft) x (4 ft) x (2 in)

we need to fix the height now so it is in the units required for the solution so lets convert it into ft.

 

Unit Conversion;

 1 in = 1/12 ft or 12 in = 1 ft

so,

(2 in) x (1 ft)/(12 in) = 2/12 ft = 1/6 ft

 

now lets put that back into our volume equation,

 

V=LWH= (18 ft) x (4 ft) x (1/6 ft) = 12 ft³

 

now lets find out how much rock we will need to fill the whole volume

using the volume equation again we find that

 

So in this case we have V= Bags x  Volume of each bag

lets rearrange this so we can find the total number of bags we need to fill the garden

 

Bags = Volume of the whole garden / Volume of each bag = (12 ft³) / (0.5 ft³) = 24 bags

 

now all we need to do is subtract the number of bags we have to find how many we need

 

Bags needed = Bags (total) - Bags (have) = (24 bags) - (10 bags) = 14 bags

 

So we found that it is Answer A. 14 bags

and we're done!

 

Best regards,

 

 

 

 

Answer 2

Hello Chandler,

 

It looks like you are asking tutors to help you answer a homework or test problem. Most tutors -- at least those with any ethics -- aren't going to help you with that. However, we will generally be happy to help you grow in authentic understanding.

 

The question being asked is actually a rather simple one. You need to figure out how many cubic feet of rocks are needed to cover the space in question, then divide it by the volume of rocks per bag.

 

If the space to be covered is 4 feet wide by 18 feet long, that is 72 square feet. What percentage of a foot is 2 inches? 2 / 12 = 0.167. This tells us that the total space to be covered will require 4 x 18 x 0.167, or 12 cubic feet. If each bag contains 1/2 cubic feet of rock, then how many total bags are needed to fill 12 cf?

 

If he already has 10 bags, then it seems that is 5 cf. At 0.5 cf/bag, how many more bags will he need?

 

Hmm. :)