Mathematics, 16.04.2020 00:24 pakabigail4796

The smallest of the three circles with center D has a radius
of 8 inches and
CB = BA = 4 inches.
What is the sum of the areas of all three circles?
O
80 rt in.
O
96 te in.?
O
20811 in.2
464rt in.

Answers: 2

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Answers

Answer from: MIC620

The sum of the areas of all three circles is 464 $\pi$ 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,

$A = \pi r^{2}$ .............................(1)

Where, r - Radius of circle

Area of smallest circle,

r = 8 inches

Equation (1) becomes,

$A_{small}$ = $\pi (8)^{2}$

= 64 $\pi$

$A_{small}$ = 64 $\pi$ squared inches

Area of middle circle,

r = 12 inches

Equation (1) becomes,

$A_{middle}$ = $\pi (12)^{2}$

= 144 $\pi$

$A_{middle}$ = 144 $\pi$ squared inches

Area of Largest circle,

r = 16 inches

Equation (1) becomes,

$A_{largest}$ = $\pi (16)^{2}$

= 256 $\pi$

$A_{Larger}$ = 256 $\pi$ squared inches

Step:3

Sum of area of three circles = Area of small circle

+ Area of middle circle + Area of larger circle

= 64 $\pi$ + 144 $\pi$ + 256 $\pi$

= 464 $\pi$ squared inches

Result:

The sum of the areas of all three circles is 464 $\pi$ squared inches, if the smallest of the three circles with center D has a radius of 8 inches and CB = BA = 4 inches.

The smallest of the three circles with center D has a radius of 8 inches and CB = BA = 4 inches. Wha

Answer from: Quest

were is the equation

Answer from: Quest

step-by-step explanation:

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The smallest of the three circles with center D has a radius
of 8 inches and
CB = BA = 4...