SOLUTION: Kevin is making a set of candles to give as a gift. The first candle is a triangular prism with a height of 17 centimeters.
The base has legs measuring 11 centimeters and 12 cen
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Question 1158208: Kevin is making a set of candles to give as a gift. The first candle is a triangular prism with a height of 17 centimeters.
The base has legs measuring 11 centimeters and 12 centimeters. The hypotenuse is about 16.3 centimeters.
Kevin makes a second candle shaped like a triangular prism, with the same height as the first candle. The base is a triangle similar to the base of the first candle, except with the shorter leg 2 centimeters longer than the shorter leg of the first candle. What are the side lengths of the base of the second candle in centimeters?
Type each measurement with a comma in between without the unit and with no period. For example: 1, 2, 3
Kevin then makes several cone-shaped candles. He uses a cone mold that has a height of 15 centimeters and a diameter of 10 centimeters. How many cubic centimeters of wax is needed to make 3 cone-shaped candles?
Only type the number.
I would appreciate if you could send me the WORK necessary as well. I have tried to answer these questions already, but as my answers were INCORRECT I am looking for help.
My previous answer to the 1st question: 13, 12, 17.7
My previous answer to the 2nd question: 392.5
This is a long passage but if anybody could explain what I got wrong as well I would really like that. Thank you so much for taking the time to answer my questions!
Found 2 solutions by ankor@dixie-net.com, solver91311:
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Kevin is making a set of candles to give as a gift.
The first candle is a triangular prism with a height of 17 centimeters.
The base has legs measuring 11 centimeters and 12 centimeters.
The hypotenuse is about 16.3 centimeters.
Kevin makes a second candle shaped like a triangular prism, with the same height as the first candle.
The base is a triangle similar to the base of the first candle, except with the
shorter leg 2 centimeters longer than the shorter leg of the first candle.
What are the side lengths of the base of the second candle in centimeters?
:
In similar triangles, the relationship between corresponding side is the same.
Short side: 13/11, find side b and c of the 2nd triangle
=
cross multiply
11b = 12*13
b =
b = 14.18
and
=
11c = 16.3*13
c =
c = 19.26
ans: 13, 14.18, 19.26
:
:
Kevin then makes several cone-shaped candles.
He uses a cone mold that has a height of 15 centimeters and a diameter of 10 centimeters.
How many cubic centimeters of wax is needed to make 3 cone-shaped candles?
:
The volume of a cone: V =
the radius: 10/2 = 5 cm
V = 3*
V = 1178.1 for three candles (your ans was for only 1 candle)
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Your error in the first problem is that you must have taken the word "similar" in the statement of the problem in the vernacular sense. You need to consider it in the plane geometry sense; that is, if two triangles are similar, then the measures of their corresponding angles are the same, and the measures of the corresponding sides are in proportion. For your problem, which said the shorter side of the new, larger triangle is 2 cm longer than the short side of the original triangle, you have the following proportions:
where 
and 
are the measures of the long leg and hypotenuse of the new triangle respectively.
First ,
Then you can either use Pythagoras, 
or the proportion 
to find the hypotenuse of the new triangular base.
I have no idea what you did wrong on the problem with the volume of a cone. I tried making every common mistake and could not come up with your answer. Looks like you just pulled a number out of your backside.
The volume of a cone is given by:
Since your diameter is 10 cm, your radius is 5 cm, so:
)
But since you want the volume of three candles, eliminate the factor of one-third:
You can do your own arithmetic.
John
My calculator said it, I believe it, that settles it
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