Answer: 1:5
Step-by-step explanation:
Given: The cost of every mirror is proportional to the cube of the mirror's radius.
i.e. [tex]\dfrac{\text{Cost of smallest mirror}}{\text{Cost of largest mirror}}=\dfrac{(\text{radii of smallest mirror}^3)}{\text{(radii of largest mirror)}^3}[/tex]
Their largest mirrors have radii of 5 meters and their smallest mirrors have radii of 1 meter.
Then,
[tex]\dfrac{\text{Cost of smallest mirror}}{\text{Cost of largest mirror}}=\dfrac{1^3}{(5)^3}=\dfrac{1}{125}[/tex]
The ratio of the total cost of 25 of the company's smallest mirrors to the cost of one of the company's largest mirrors will be:
[tex]\dfrac{\text{Cost of 25 smallest mirror}}{\text{Cost of largest mirror}}=\dfrac{25\times 1}{125}=\dfrac{1}{5}[/tex]
Hence, the ratio of the total cost of 25 of the company's smallest mirrors to the cost of one of the company's largest mirrors = 1:5 .
