Given:
Radii of two spheres are 3 cm and 4.5 cm respectively.
Surface area of the smaller sphere is 367 cm.
To find:
The surface area of the larger sphere.
Solution:
We know that, area of similar spheres is proportional to the square of there radii.
[tex]\dfrac{A_1}{A_2}=\dfrac{(r_1)^2}{(r_2)^2}[/tex]
On substituting the values, we get
[tex]\dfrac{367}{A_2}=\dfrac{(3)^2}{(4.5)^2}[/tex]
[tex]\dfrac{367}{A_2}=\dfrac{9}{20.25}[/tex]
On cross multiplication, we get
[tex](367)(20.25)=9A_2[/tex]
[tex]7431.75=9A_2[/tex]
Divide both sides by 9.
[tex]\dfrac{7431.75}{9}=A_2[/tex]
[tex]825.75 =A_2[/tex]
Therefore, the area of larger sphere is 825.75 cm².
Note: All options are incorrect.
