Respuesta :
When you have a problem like this one, you have to remember that the linear relationship between the 2 similar objects is one-to-one. To find the ratio of their areas you have to square each of these one-to-one measures. If the one-to-one ratio is 4/7, then the ratio of their areas is found by squaring both those numbers to get 16/49. Obviously 16 is less than 49 so we have our ratio set up with smaller "stuff" on top and larger on bottom. Work it like a proportion now:[tex] \frac{16}{49} = \frac{220}{x} [/tex] where x is the area of the larger object. Cross-multiply to get 16x = 10780 and x = 673.75.
Using the concept of a ratio and proportion to solve the problem. Then the surface area of the larger can is 673.75 square cm.
What are ratio and proportion?
A ratio is an ordered couple of numbers a and b, written as a/b where b can not equal 0. A proportion is an equation in which two ratios are set equal to each other.
Given
The ratio of the corresponding linear measures of two similar cans of fruit is 4 to 7.
The smaller can has a surface area of 220 square centimeters.
Let x be the larger can and y be the smaller can. Then
[tex]\rm \dfrac{r_2}{r_1} =\dfrac{h_2}{h_1} = \dfrac{7}{4}[/tex]
Then the ratio of their area is given by
[tex]\rm \dfrac{Area \ of \ larger \ can }{Area\ of \ smaller \ can} = \dfrac{2* \pi *r_2h_2}{2 * \pi * r_1 h_1}\\\\\\\dfrac{Area \ of \ larger \ can }{Area\ of \ smaller \ can} = \dfrac{2* \pi *(\frac{7}{4})r_1(\frac{7}{4})h_1}{2 * \pi * r_1 h_1}\\\\\\\dfrac{Area \ of \ larger \ can }{220} = \dfrac{49}{16}\\\\\\Area \ of \ larger \ can = 673.75[/tex]
Thus, the surface area of the larger can is 673.75 square cm.
More about the ratio and the proportion link is given below.
https://brainly.com/question/165414
