Respuesta :
We have been given that two rectangular prisms, M and N, are mathematically similar. The volumes of M and N are 17 cm^3 and 136 cm^3, respectively. The height of N is 18 cm. We are asked to find the height of M.
First of all, we will find the ratio between sides of rectangle M and N using proportions.
[tex]\frac{\text{Side of N}}{\text{Side of M}}=\frac{\text{ Volume of N}}{\text{ Volume of M}}[/tex]
[tex]\frac{\text{Side of N}}{\text{Side of M}}=\frac{136\text{ cm}^3}{17\text{ cm}^3}[/tex]
[tex]\frac{\text{Side of N}}{\text{Side of M}}=\frac{8\text{ cm}^3}{1\text{ cm}^3}[/tex]
Now we will take cube root on right side to find length in cm.
[tex]\frac{\text{Side of N}}{\text{Side of M}}=\frac{\sqrt[3]{\text{8 cm}^3}}{\sqrt[3]{\text{1 cm}^3}}[/tex]
[tex]\frac{\text{Side of N}}{\text{Side of M}}=\frac{\text{2 cm}}{\text{1 cm}}[/tex]
Therefore, sides of rectangle N is 2 times greater than sides of rectangle M.
To find height of rectangle M, we will divide side of rectangle N by 2.
[tex]\text{Height of rectangle M}=\frac{18}{2}=9[/tex]
Therefore, height of rectangle M is 9 cm.
