PIECES OF SOAP ARE PACKED IN A CUBOID CONTAINER MEASURING 36CM BY 24CM BY 18CM. EACH PIECE OF SOAP IS SIMILAR TO THE CONTAINER.IF THE LINEAR SCALE FACTOR BETWEEN THE CONTAINER AND THE SOAP IS ONE OVER SIX,FIND THE VOLUME OF EACH PIECE OF SOAP.
volume= 24/6 x 36/6 x 18/6= 4x6x3 cm^3
volume changes as the cube of the scale. So, each piece as 1/6^3 the volume of the container.
Good answer
To find the volume of each piece of soap, we need to determine the linear scale factor between the container and the soap.
The linear scale factor is the ratio of corresponding lengths between the container and the soap.
Given that the linear scale factor is one over six, it means that for every 1 unit of length on the container, the soap has 1/6 units of length.
To find the volume of each piece of soap, we can use the formula:
Volume = (Length)^3
First, let's determine the length of the soap. We know that the length of the container is 36 cm. Since the linear scale factor is 1/6, the length of the soap would be:
Length of the soap = Linear scale factor * Length of the container
= (1/6) * 36 cm
= 6 cm
Next, we substitute the length of the soap into the volume formula:
Volume of each piece of soap = (Length)^3
= (6 cm)^3
= 6 cm *6 cm * 6 cm
= 216 cm^3
Therefore, the volume of each piece of soap is 216 cm^3.