Question

the formula v = lwh is used to find the volume of a box. if the length of a box is increased 5 times, the width is increased 4 times, and the height is doubled, how does this affect the volume? select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. the volume is decreased by (type a whole number.) b. the volume is increased by (type a whole number.) c. the volume is multiplied by (type a whole number.)

Explanation:

Step1: Identify initial and new volume formulas

The initial volume $V_1 = L_1W_1H_1$. The new length $L_2 = 5L_1$, new width $W_2=4W_1$, new height $H_2 = 2H_1$. The new volume $V_2=L_2W_2H_2$.

Step2: Substitute new - dimensions into volume formula

$V_2=(5L_1)\times(4W_1)\times(2H_1)$.

Step3: Simplify the new - volume formula

$V_2 = 5\times4\times2\times L_1W_1H_1=40L_1W_1H_1$. Since $V_1 = L_1W_1H_1$, the volume is multiplied by 40.

Answer:

C. The volume is multiplied by 40.