prism has total surface area of 360 m2 and volume of 60 m3.
If the length, width, and height are reduced to half their original sizes, what will be the following?
To find out what will happen to the measurements if the length, width, and height are reduced to half their original sizes, we need to use the formulae for the total surface area and volume of a rectangular prism.
The formula for the total surface area of a rectangular prism is given by:
Surface Area = 2lw + 2lh + 2wh
And the formula for the volume of a rectangular prism is given by:
Volume = lwh
Let's first consider the effect on the total surface area if the length, width, and height are halved.
If the length, width, and height are all halved, the new values can be represented by l/2, w/2, and h/2, respectively.
The new surface area, which we'll call S', can be calculated by substituting these new values into the surface area formula:
S' = 2(l/2)(w/2) + 2(l/2)(h/2) + 2(w/2)(h/2)
= (lw + lh + wh)/2
So, the new total surface area will be half of the original total surface area.
Now let's consider the effect on the volume if the length, width, and height are halved.
Using the new values l/2, w/2, and h/2, the new volume, which we'll call V', can be calculated:
V' = (l/2)(w/2)(h/2)
= (lwh)/8
So, the new volume will be 1/8 (or one-eighth) of the original volume.
In summary, if the length, width, and height of a prism are reduced to half their original sizes, the total surface area will be halved, and the volume will be one-eighth the original volume.