Question

dimensions of box 1: $x$ by $3x$ by $x^3$
the volume of box 1 is given by:
$\bigcirc$ $3x^7$
$\bigcirc$ $3x^6$
$\bigcirc$ $3x^5$
$\bigcirc$ $5x^3$
done

Explanation:

Step1: Recall volume formula for box

The volume \( V \) of a rectangular box is the product of its length, width, and height: \( V = l \times w \times h \)

Step2: Substitute given dimensions

Substitute \( l = x \), \( w = 3x \), \( h = x^3 \):
\( V = x \times 3x \times x^3 \)

Step3: Multiply coefficients and variables

First multiply the coefficients: \( 1 \times 3 = 3 \)
Then multiply the variables using exponent rule \( x^a \times x^b = x^{a+b} \): \( x^1 \times x^1 \times x^3 = x^{1+1+3} = x^5 \)
Combine results: \( V = 3x^5 \)

Answer:

\( 3x^5 \) (the third option)