I am having difficulty understanding this word problem ifsomeone can please help
ID: 3096214 • Letter: I
Question
I am having difficulty understanding this word problem ifsomeone can please help me that would be great. Thank you. Word problem: Ivan has mixed cake ingredients in a largecylinder bowl, whose radius is 12'' and whose height is 8''. He hasfive large cake pans measuring 12'' x 18'' x 3'', medium ones measuring 9''x13''x3'' and three small ones measuring8''x8''x3''. He wants to use all the large and medium pans, and thesmall ones for the left over. How many large, medium, and smallcake pans can be filled to a height of 2'' from the mixed cakeingredients? I am having difficulty understanding this word problem ifsomeone can please help me that would be great. Thank you. Word problem: Ivan has mixed cake ingredients in a largecylinder bowl, whose radius is 12'' and whose height is 8''. He hasfive large cake pans measuring 12'' x 18'' x 3'', medium ones measuring 9''x13''x3'' and three small ones measuring8''x8''x3''. He wants to use all the large and medium pans, and thesmall ones for the left over. How many large, medium, and smallcake pans can be filled to a height of 2'' from the mixed cakeingredients?Explanation / Answer
The idea here is to figure out how many pans he will fill up,starting with the large pans, then the medium, then the smallones. The first step is to figure out how much cake mix you havetotal. You can find out how much cake mix he has bycalculating the volume of the bowl. The volume of a cylinderis V = *r2*h ( is pi, r theradius, and h the height). This will give you a total volumeof cake mix in cubic inches (in3). Let's call thetotal volume Vtot. Next, you need to find out how much cake mix goes into thelarge pans. To find the volume of each large pan, use theequation for a rectangular prism (rectangular box). V = l * w * h l is the length, w is the width, and h is the height. The trick to remember is that he is only filling each panto 2" high! (so your height will not be the actual height ofthe pan....only how high he's filling it). Let's call thevolume of each large pan Vlarge. Now, find the volume of the medium pans in the same way as thelarge ones (use V = l * w * h, and use the length and width givento you for the medium pans. The height is still only2"!). Call this volumeVmedium. The problem says that he wants to use the large and mediumpans first. It also tells us that he has 5 large pans and ??medium ones (you forget to tell how many medium ones :). So,we can figure out how much cake mix is left for the smallpans: volume of leftover cake mix for the small pans =Vtot - 5*Vlarge -??*Vmedium (where ?? indicates the number of medium pans that Ivanhas) Let's call this leftover amountVleft. Now, we need to figure out how many small pans it will take touse up all the leftover mix. Figure out the volume of mixused up by each small pan (V = l * w * h). h is still 2"since that's how high he's filling each pan! Call this volumeVsmall. Finally, we can figure out how many small pans Ivanneeds: number of small pans =Vleft/Vsmall Obviously, round up to the nearest whole number since he won'tuse a part of a pan :) Obviously, round up to the nearest whole number since he won'tuse a part of a pan :)Related Questions
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