Answer:
The surface area is divided by 25.
Step-by-step explanation:
The radius of a sphere is given as 15 m.
To obtain the surface area of the original sphere, substitute the radius length into the formula for the surface area of a sphere, S=4πr2.
S=4π(15)2=(4)(225)π=900π
The surface area of the original sphere is 900π m2.
To find the radius of the new sphere divide the radius of the original sphere by 5.
r=155=3
The radius of the new sphere is 3 m.
To obtain the surface area of the new sphere, substitute the radius length into the formula for the surface area of a sphere, S=4πr2.
S=4π(3)2=(4)(9)π=36π
The surface area is 36π m2.
Notice that 900π=25(36π). The surface area of the second sphere is 52=25 times less than the original surface area. The surface area of a sphere changes by the square of the factor that the radius changes.
Therefore, the surface area is divided by 25.
