Evan and Marshall are having a debate. Evan contends that the Pantheon is larger than the Parthenon in terms of area. Marshall contends the opposite. To settle their debate, they find satellite images of both ancient temples and juxtapose them on a single coordinate grid (shown below).

Looking at the graph, the radius of the Pantheon is

30

m

30m30, start text, m, end text. Let's find the area of the Pantheon, rounding our result to the nearest square meter.

area of the Pantheon

=

π

r

2

=

π

⋅

3

0

2

≈

2827

m

area of the Pantheon

=πr

2

=π⋅30

2

≈2827m

Hint #22 / 3

To determine the area of the Parthenon, we'll need to find its length and width. Let's use the distance formula to find the length from

(

−

15

,

−

45

)

(−15,−45)left parenthesis, minus, 15, comma, minus, 45, right parenthesis to

(

45

,

−

25

)

(45,−25)left parenthesis, 45, comma, minus, 25, right parenthesis.

l

=

(

Δ

x

)

2

+

(

Δ

y

)

2

=

(

45

−

(

−

15

)

)

2

+

(

−

25

−

(

−

45

)

)

2

=

(

60

)

2

+

(

20

)

2

=

3600

+

400

=

4000

l

=

(Δx)

2

+(Δy)

2

=

(45−(−15))

2

+(−25−(−45))

2

=

(60)

2

+(20)

2

=

3600+400

=

4000

We can use the distance formula to find the width of the Parthenon as well.

w

=

1000

w=

1000

w, equals, square root of, 1000, end square root

area of Parthenon

=

l

⋅

w

=

2000

m

2

area of Parthenon=l⋅w=2000m

2

start text, a, r, e, a, space, o, f, space, P, a, r, t, h, e, n, o, n, end text, equals, l, dot, w, equals, 2000, start text, m, end text, squared

Hint #33 / 3

The area of the Pantheon is

2827

m

2

2827m 2 2827, start text, m, end text, squared.

The area of the Parthenon is 2000m2

2000m 2

2000, start text, m, end text, squared.

Evan should win the debate.Step-by-step explanation:

256π units²   (answer b)

step-by-step explanation:

the formula for the surface area of a sphere of radius r

is             a = 4πr²

and so, if r = 8 units, then the surface area is:

a = 4π(8 units)² = 256π units²   (answer b)