Final answer:
To find the height of the wax in the mold, we calculate the volume of the original wax block (18 in³) and divide it by the base area of the mold (33 in²), resulting in a height of approximately 0.545 inches.
Step-by-step explanation:
The student's question involves calculating the height of wax in a mold, given the volume of the original block of wax and the base area of the mold. To solve this, we need to find the volume of the original block of wax and then use this volume to find the height of the wax in the mold.
First, we calculate the volume of the block of wax using the formula for the volume of a rectangular prism, which is length (×) width (×) height. The wax block's dimensions are given as 2¼ inches by 2 inches by 4 inches. Since 2¼ inches equal 2.25 inches, the volume of the block is 2.25 in × 2 in × 4 in = 18 in³.
Next, we use the volume of the wax (18 in³) and the base area of the mold (33 in²) to determine the height of the wax in the mold. By the principle of conservation of volume, the volume of the wax will remain the same after melting and pouring into the mold. Thus, the volume of the wax equals the volume of the mold, which leads us to the equation 18 in³ = 33 in² × height.
To find the height, we divide the volume of the wax by the base area of the mold: height = 18 in³ / 33 in². This gives us a height of 0.545 in, which is the height of the wax in the mold.