A rectangular prism has a length of 4.2 cm, a width of 5.8 cm, and a height of 9.6 cm. A similar prism has a length of 14.7 cm, a width of 20.3 cm, and a height of 33.6 cm.
The dimensions of the smaller prism are each multiplied by what factor to produce the corresponding dimensions of the larger prism?
To determine the factor by which the dimensions of the smaller prism are multiplied to produce the corresponding dimensions of the larger prism, we need to compare the corresponding sides of both prisms.
Let's start by comparing the lengths of the two prisms:
Length of the larger prism = 14.7 cm
Length of the smaller prism = 4.2 cm
To find the factor of multiplication, we divide the length of the larger prism by the length of the smaller prism:
14.7 cm ÷ 4.2 cm ≈ 3.5
Therefore, the length of the smaller prism is multiplied by a factor of about 3.5 to produce the length of the larger prism.
Now, let's compare the widths:
Width of the larger prism = 20.3 cm
Width of the smaller prism = 5.8 cm
Similar to before, we divide the width of the larger prism by the width of the smaller prism:
20.3 cm ÷ 5.8 cm ≈ 3.5
Again, we find that the width of the smaller prism is multiplied by a factor of about 3.5 to produce the width of the larger prism.
Finally, let's compare the heights:
Height of the larger prism = 33.6 cm
Height of the smaller prism = 9.6 cm
Dividing the height of the larger prism by the height of the smaller prism:
33.6 cm ÷ 9.6 cm ≈ 3.5
As previously, we conclude that the height of the smaller prism is multiplied by a factor of about 3.5 to produce the height of the larger prism.
In summary, the dimensions of the smaller prism are each multiplied by a factor of about 3.5 to produce the corresponding dimensions of the larger prism.
compare the two lengths of the corresponding dimenstions:
lengths: 14.7/4.2 = 3.5
widths : 20.3/5.8 = 3.5
heights: 33.6/9.6 = 3.5
well, how about that ??