Question

There are two boxes in a storage unit. The volume of the first box is 4x + 4x^2 cubic units. The volume of the second box is 6x^3 - 18x^2 cubic units.The total volume of both boxes is:

a) 10x^3−14x^2+4x
b) 10x^3+14x^2−4x
c) 10x^3−14x^2−4x
d) 10x^3+14x^2+4x

Answer 1

To find the total volume of both boxes in the storage unit, add the volume of each box and simplify the expression. The combined volume is the sum of 4x + 4x^2 and 6x^3 - 18x^2, which simplifies to 6x^3 - 14x^2 + 4x cubic units. Therefore, the correct answer is 10x^3−14x^2+4x.

Step-by-step explanation:

The student asked about calculating the combined volume of two boxes located in a storage unit. The first box has a volume given by the expression 4x + 4x^2 cubic units, and the second box has a volume given by 6x^3 - 18x^2 cubic units. To find the total volume of both boxes, we simply add the volumes of each box:

Volume of the first box: 4x + 4x^2 cubic units
Volume of the second box: 6x^3 - 18x^2 cubic units
Total Volume = (4x + 4x^2) + (6x^3 - 18x^2) cubic units

Simplifying the expression by combining like terms yields the final expression for the total volume:
Total Volume = 6x^3 - 14x^2 + 4x cubic units

Hence, the correct answer is option a) 10x^3−14x^2+4x.