The ratio of areas is proportional to the ratio of the square of the radii. The area of the larger dish is 72 square inches.
Important information:
Area of a small circular dish is 8 square inches.
The radius of the larger dish is tripled than the smaller dish.
We need to find the area of the larger dish.
Let [tex]r_1,r_2[/tex] are radius and [tex]A_1,A_2[/tex] are areas of smaller and larger dishes respectively.
[tex]\dfrac{(r_1)^2}{(r_2)^2}=\dfrac{A_1}{A_2}[/tex]
[tex]\dfrac{(r_1)^2}{(3r_1)^2}=\dfrac{8}{A_2}[/tex]
[tex]\dfrac{(r_1)^2}{9(r_1)^2}=\dfrac{8}{A_2}[/tex]
[tex]\dfrac{1}{9}=\dfrac{8}{A_2}[/tex]
On cross-multiplication, we get
[tex]A_2=9\times 8[/tex]
[tex]A_2=72[/tex]
Therefore, the area of the larger dish is 72 square inches.
Find out more about 'Area of similar figures:' here:
https://brainly.com/question/15481281
