Question

a box is to be constructed with a rectangular base and a height of h cm. the length, l, of the box is 10 cm, and the width, w, is twice the height. which quadratic equation best models the volume of the box?
v = lwh
○ v = 20h
○ v = 20h²
○ v = 100h
○ v = 100h²

Explanation:

Step1: Determine the width in terms of height

The width \( w \) is twice the height \( h \), so \( w = 2h \).

Step2: Substitute length, width, and height into volume formula

The volume formula for a rectangular box is \( V = lwh \). We know \( l = 10 \) cm, \( w = 2h \), and \( h = h \). Substituting these values in, we get \( V = 10\times(2h)\times h \).

Step3: Simplify the expression

Simplify \( 10\times(2h)\times h \). First, multiply 10 and 2 to get 20, then multiply by \( h\times h = h^{2} \). So \( V = 20h^{2} \).

Answer:

\( V = 20h^{2} \) (corresponding to the option \( V = 20h^{2} \))