Calculate Cuboid Volume: Finding Volume in Terms of X with Dimensions (5+X, 4+X, 7)

Look at the following cuboid.

Express the volume of the cuboid in terms of X.

Video Solution

Solution Steps

00:00 Express the volume of the box using X

00:03 We'll use the formula for calculating box volume

00:07 Height times length times width

00:10 We'll substitute appropriate values and solve to find the volume expression

00:28 Open parentheses properly, multiply each factor by each factor

00:53 Open parentheses properly, multiply by each factor

01:13 And this is the solution to the question

Step-by-Step Solution

To solve this problem, we'll begin by writing down the formula for the volume of a cuboid. The volume $V$ is given by:

V = \text{length} \times \text{width} \times \text{height}

Given dimensions are:

Substituting these into the formula gives:

V = (5 + X) \times (4 + X) \times 7

First, expand the product of the first two terms:

(5 + X)(4 + X) = 5 \times 4 + 5 \times X + X \times 4 + X \times X

= 20 + 5X + 4X + X^2

= X^2 + 9X + 20

Now multiply this by the height (7):

V = (X^2 + 9X + 20) \times 7

= 7 \times X^2 + 7 \times 9X + 7 \times 20

= 7X^2 + 63X + 140

Thus, the volume of the cuboid in terms of $X$ is:

$7X^2 + 63X + 140$