Volume of a rectangular prism after t days
$begingroup$
I'm really stuck on this question and would like some direction.
An iceberg approximates the shape of a rectangular prism and is about 800 m long, 400 m wide and 120 m thick. As it moves into warmer water it melts evenly by 1 m per day along each measurement.
Find the volume of the iceberg after 't' days
The answer in the textbook states:
$$V(t) = 38 400 000 − 464 000t + 1320t^2 − t^3$$
Any suggestion would be great
derivatives volume
asked Dec 31 '18 at 9:20
user415903user415903
295
$endgroup$
add a comment |
$begingroup$
I'm really stuck on this question and would like some direction.
An iceberg approximates the shape of a rectangular prism and is about 800 m long, 400 m wide and 120 m thick. As it moves into warmer water it melts evenly by 1 m per day along each measurement.
Find the volume of the iceberg after 't' days
The answer in the textbook states:
$$V(t) = 38 400 000 − 464 000t + 1320t^2 − t^3$$
Any suggestion would be great
derivatives volume
asked Dec 31 '18 at 9:20
user415903user415903
295
$endgroup$
2
$begingroup$
I’m sure that you’ll be able to tell us your thoughts about the question.
$endgroup$
– mathcounterexamples.net
Dec 31 '18 at 9:23
3
$begingroup$
$V=(800-t)(400-t)(120-t)$
$endgroup$
– Mohammad Zuhair Khan
Dec 31 '18 at 9:25
$begingroup$
@mathcounterexamples.net I was initally thinking could this be a related rates question, but it doesn't seem to work out. I then tried using simultaneous equations using volume and the surface area formula but then again I don't think that is the right direction
$endgroup$
– user415903
Dec 31 '18 at 9:28
$begingroup$
@MohammadZuhairKhan wow I do not understand how I did not think like that, thank you so much!
$endgroup$
– user415903
Dec 31 '18 at 9:32
$begingroup$
@user415903 At least tell us what is the volume of a rectangular prism knowing its dimensions.
$endgroup$
– mathcounterexamples.net
Dec 31 '18 at 9:32
add a comment |
$begingroup$
I'm really stuck on this question and would like some direction.
An iceberg approximates the shape of a rectangular prism and is about 800 m long, 400 m wide and 120 m thick. As it moves into warmer water it melts evenly by 1 m per day along each measurement.
Find the volume of the iceberg after 't' days
The answer in the textbook states:
$$V(t) = 38 400 000 − 464 000t + 1320t^2 − t^3$$
Any suggestion would be great
derivatives volume
asked Dec 31 '18 at 9:20
user415903user415903
295
$endgroup$
I'm really stuck on this question and would like some direction.
An iceberg approximates the shape of a rectangular prism and is about 800 m long, 400 m wide and 120 m thick. As it moves into warmer water it melts evenly by 1 m per day along each measurement.
Find the volume of the iceberg after 't' days
The answer in the textbook states:
$$V(t) = 38 400 000 − 464 000t + 1320t^2 − t^3$$
Any suggestion would be great
derivatives volume
derivatives volume
asked Dec 31 '18 at 9:20
user415903user415903
295
asked Dec 31 '18 at 9:20
user415903user415903
295
asked Dec 31 '18 at 9:20
user415903user415903
295
asked Dec 31 '18 at 9:20
user415903user415903
295
asked Dec 31 '18 at 9:20
user415903user415903
295
295
2
$begingroup$
I’m sure that you’ll be able to tell us your thoughts about the question.
$endgroup$
– mathcounterexamples.net
Dec 31 '18 at 9:23
3
$begingroup$
$V=(800-t)(400-t)(120-t)$
$endgroup$
– Mohammad Zuhair Khan
Dec 31 '18 at 9:25
$begingroup$
@mathcounterexamples.net I was initally thinking could this be a related rates question, but it doesn't seem to work out. I then tried using simultaneous equations using volume and the surface area formula but then again I don't think that is the right direction
$endgroup$
– user415903
Dec 31 '18 at 9:28
$begingroup$
@MohammadZuhairKhan wow I do not understand how I did not think like that, thank you so much!
$endgroup$
– user415903
Dec 31 '18 at 9:32
$begingroup$
@user415903 At least tell us what is the volume of a rectangular prism knowing its dimensions.
$endgroup$
– mathcounterexamples.net
Dec 31 '18 at 9:32
add a comment |
2
$begingroup$
I’m sure that you’ll be able to tell us your thoughts about the question.
$endgroup$
– mathcounterexamples.net
Dec 31 '18 at 9:23
3
$begingroup$
$V=(800-t)(400-t)(120-t)$
$endgroup$
– Mohammad Zuhair Khan
Dec 31 '18 at 9:25
$begingroup$
@mathcounterexamples.net I was initally thinking could this be a related rates question, but it doesn't seem to work out. I then tried using simultaneous equations using volume and the surface area formula but then again I don't think that is the right direction
$endgroup$
– user415903
Dec 31 '18 at 9:28
$begingroup$
@MohammadZuhairKhan wow I do not understand how I did not think like that, thank you so much!
$endgroup$
– user415903
Dec 31 '18 at 9:32
$begingroup$
@user415903 At least tell us what is the volume of a rectangular prism knowing its dimensions.
$endgroup$
– mathcounterexamples.net
Dec 31 '18 at 9:32
2
2
$begingroup$
I’m sure that you’ll be able to tell us your thoughts about the question.
$endgroup$
– mathcounterexamples.net
Dec 31 '18 at 9:23
$begingroup$
I’m sure that you’ll be able to tell us your thoughts about the question.
$endgroup$
– mathcounterexamples.net
Dec 31 '18 at 9:23
3
3
$begingroup$
$V=(800-t)(400-t)(120-t)$
$endgroup$
– Mohammad Zuhair Khan
Dec 31 '18 at 9:25
$begingroup$
$V=(800-t)(400-t)(120-t)$
$endgroup$
– Mohammad Zuhair Khan
Dec 31 '18 at 9:25
$begingroup$
@mathcounterexamples.net I was initally thinking could this be a related rates question, but it doesn't seem to work out. I then tried using simultaneous equations using volume and the surface area formula but then again I don't think that is the right direction
$endgroup$
– user415903
Dec 31 '18 at 9:28
$begingroup$
@mathcounterexamples.net I was initally thinking could this be a related rates question, but it doesn't seem to work out. I then tried using simultaneous equations using volume and the surface area formula but then again I don't think that is the right direction
$endgroup$
– user415903
Dec 31 '18 at 9:28
$begingroup$
@MohammadZuhairKhan wow I do not understand how I did not think like that, thank you so much!
$endgroup$
– user415903
Dec 31 '18 at 9:32
$begingroup$
@MohammadZuhairKhan wow I do not understand how I did not think like that, thank you so much!
$endgroup$
– user415903
Dec 31 '18 at 9:32
$begingroup$
@user415903 At least tell us what is the volume of a rectangular prism knowing its dimensions.
$endgroup$
– mathcounterexamples.net
Dec 31 '18 at 9:32
$begingroup$
@user415903 At least tell us what is the volume of a rectangular prism knowing its dimensions.
$endgroup$
– mathcounterexamples.net
Dec 31 '18 at 9:32
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Trying this question from the basics would be helpful.
The volume of a rectangular prism is the product of the three sides.
The initial sides are $800,400,120$ respectively.
Since each sides reduces by $1$m in one day, after $t$ days there will be a reduction of $t$ meters in each side.
Therefore, the sides of the prism, at the end of $t$ days, will be $800-t,400-t,120-t$. Therefore the volume will be the product of these three i.e. $(800-t)(400-t)(120-t)$. Expanding the products leads to the given answer.
answered Dec 31 '18 at 9:34
астон вілла олоф мэллбэргастон вілла олоф мэллбэрг
38.9k33477
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add a comment |
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$begingroup$
Trying this question from the basics would be helpful.
The volume of a rectangular prism is the product of the three sides.
The initial sides are $800,400,120$ respectively.
Since each sides reduces by $1$m in one day, after $t$ days there will be a reduction of $t$ meters in each side.
Therefore, the sides of the prism, at the end of $t$ days, will be $800-t,400-t,120-t$. Therefore the volume will be the product of these three i.e. $(800-t)(400-t)(120-t)$. Expanding the products leads to the given answer.
answered Dec 31 '18 at 9:34
астон вілла олоф мэллбэргастон вілла олоф мэллбэрг
38.9k33477
$endgroup$
add a comment |
$begingroup$
Trying this question from the basics would be helpful.
The volume of a rectangular prism is the product of the three sides.
The initial sides are $800,400,120$ respectively.
Since each sides reduces by $1$m in one day, after $t$ days there will be a reduction of $t$ meters in each side.
Therefore, the sides of the prism, at the end of $t$ days, will be $800-t,400-t,120-t$. Therefore the volume will be the product of these three i.e. $(800-t)(400-t)(120-t)$. Expanding the products leads to the given answer.
answered Dec 31 '18 at 9:34
астон вілла олоф мэллбэргастон вілла олоф мэллбэрг
38.9k33477
$endgroup$
add a comment |
$begingroup$
Trying this question from the basics would be helpful.
The volume of a rectangular prism is the product of the three sides.
The initial sides are $800,400,120$ respectively.
Since each sides reduces by $1$m in one day, after $t$ days there will be a reduction of $t$ meters in each side.
Therefore, the sides of the prism, at the end of $t$ days, will be $800-t,400-t,120-t$. Therefore the volume will be the product of these three i.e. $(800-t)(400-t)(120-t)$. Expanding the products leads to the given answer.
answered Dec 31 '18 at 9:34
астон вілла олоф мэллбэргастон вілла олоф мэллбэрг
38.9k33477
$endgroup$
Trying this question from the basics would be helpful.
The volume of a rectangular prism is the product of the three sides.
The initial sides are $800,400,120$ respectively.
Since each sides reduces by $1$m in one day, after $t$ days there will be a reduction of $t$ meters in each side.
Therefore, the sides of the prism, at the end of $t$ days, will be $800-t,400-t,120-t$. Therefore the volume will be the product of these three i.e. $(800-t)(400-t)(120-t)$. Expanding the products leads to the given answer.
answered Dec 31 '18 at 9:34
астон вілла олоф мэллбэргастон вілла олоф мэллбэрг
38.9k33477
answered Dec 31 '18 at 9:34
астон вілла олоф мэллбэргастон вілла олоф мэллбэрг
38.9k33477
answered Dec 31 '18 at 9:34
астон вілла олоф мэллбэргастон вілла олоф мэллбэрг
38.9k33477
answered Dec 31 '18 at 9:34
астон вілла олоф мэллбэргастон вілла олоф мэллбэрг
38.9k33477
38.9k33477
add a comment |
add a comment |
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2
$begingroup$
I’m sure that you’ll be able to tell us your thoughts about the question.
$endgroup$
– mathcounterexamples.net
Dec 31 '18 at 9:23
3
$begingroup$
$V=(800-t)(400-t)(120-t)$
$endgroup$
– Mohammad Zuhair Khan
Dec 31 '18 at 9:25
$begingroup$
@mathcounterexamples.net I was initally thinking could this be a related rates question, but it doesn't seem to work out. I then tried using simultaneous equations using volume and the surface area formula but then again I don't think that is the right direction
$endgroup$
– user415903
Dec 31 '18 at 9:28
$begingroup$
@MohammadZuhairKhan wow I do not understand how I did not think like that, thank you so much!
$endgroup$
– user415903
Dec 31 '18 at 9:32
$begingroup$
@user415903 At least tell us what is the volume of a rectangular prism knowing its dimensions.
$endgroup$
– mathcounterexamples.net
Dec 31 '18 at 9:32