The sum of the areas of all three circles is 464[tex]\pi[/tex] squared inches, if the smallest of the three circles with center D has a radius of 8 inches and CB = BA = 4 inches.
Step-by-step explanation:
The given is,
Three circles,
Smallest circle with center D has a radius of 8 inches.
CB = BA = 4 inches
Step:1
Ref the attachment,
Radius of smallest circle(DC) = 8 inches
Radius of middles circle (DB),
DB = BC + DC = 4 + 8 = 12 inches
Radius of largest circle (DA),
DA = AB + BC + CD = 4 + 4 + 8
DA = 16 inches
Step:2
Formula for area of circle,
[tex]A = \pi r^{2}[/tex].............................(1)
Where, r - Radius of circle
Area of smallest circle,
r = 8 inches
Equation (1) becomes,
[tex]A_{small}[/tex] = [tex]\pi (8)^{2}[/tex]
= 64[tex]\pi[/tex]
[tex]A_{small}[/tex] = 64[tex]\pi[/tex] squared inches
Area of middle circle,
r = 12 inches
Equation (1) becomes,
[tex]A_{middle}[/tex] = [tex]\pi (12)^{2}[/tex]
= 144[tex]\pi[/tex]
[tex]A_{middle}[/tex] = 144[tex]\pi[/tex] squared inches
Area of Largest circle,
r = 16 inches
Equation (1) becomes,
[tex]A_{largest}[/tex] = [tex]\pi (16)^{2}[/tex]
= 256[tex]\pi[/tex]
[tex]A_{Larger}[/tex] = 256[tex]\pi[/tex] squared inches
Step:3
Sum of area of three circles = Area of small circle
+ Area of middle circle + Area of larger circle
= 64[tex]\pi[/tex] + 144[tex]\pi[/tex] + 256[tex]\pi[/tex]
= 464[tex]\pi[/tex] squared inches
Result:
The sum of the areas of all three circles is 464[tex]\pi[/tex] squared inches, if the smallest of the three circles with center D has a radius of 8 inches and CB = BA = 4 inches.
Answer:
464 [tex]\pi[/tex] [tex]in.^{2}[/tex]
Step-by-step explanation:
did it on edge
