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
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.