Question

warm - up: boxes. which one doesnt belong? explain your reasoning. a. length: 4 cm, width: 8 cm, height: 10 cm. b. 10 cm, 8 cm, 2 cm. c. 20 in, 4 in, 4 in. d. v = 320 cm³, 4x cm, x + 1 cm, x cm

Explanation:

Step1: Calculate volumes of a, b, c

Volume of a rectangular - prism is $V = l\times w\times h$.
For a: $V_a=4\times8\times10 = 320$ $cm^3$.
For b: $V_b=8\times2\times10 = 160$ $cm^3$.
For c: First convert inches to centimeters. 1 inch = 2.54 cm. But if we just consider the numerical values of the sides in inches, $V_c = 4\times4\times20=320$ $in^3$.
For d: $V_d=(x + 1)\times x\times4x=4x^3+4x^2$. Given $V_d = 320$ $cm^3$, so $4x^3+4x^2=320$, $x^3 + x^2=80$.

Step2: Analyze the non - matching one

Options a, c, and d have a volume of 320 (either in $cm^3$ or the equation for d results in a volume of 320 $cm^3$ when solved for x), while option b has a volume of 160 $cm^3$.

Answer:

b