Given:
Two jugs are similar. The smaller jug has radius 4 cm and the bigger jug has radius 6 cm and surface area 125 cm².
To find:
The area of the smaller jug.
Solution:
If two figures are similar, then the ratio of their areas is proportional to the square of the corresponding sides of the figures.
Two jugs are similar. So,
[tex]\dfrac{\text{Area of smaller jug}}{\text{Area of bigger jug}}=\dfrac{(\text{Radius of smaller jug})^2}{(\text{Radius of bigger jug})^2}[/tex]
[tex]\dfrac{\text{Area of smaller jug}}{125}=\dfrac{(4)^2}{(6)^2}[/tex]
[tex]\dfrac{\text{Area of smaller jug}}{125}=\dfrac{16}{36}[/tex]
[tex]\text{Area of smaller jug}=\dfrac{4}{9}\times 125[/tex]
[tex]\text{Area of smaller jug}\approx 55.56[/tex]
Therefore, the area of the smaller jug is about 55.56 cm².
