A plane intersects the center of a sphere with a volume of about 9,202.8 m3. What is
the area of the cross section? Round to the
nearest tenth.

530.66

Step-by-step explanation:

The computation of the area of the cross section is shown below

Given that

Volume = 9208 m^3

Now let us assume the radius be r

So volume = 4 ÷ 3 πr^3

9202.8 × 3 ÷ 4π = r^3

27,608.4 ÷ 4 × 3.14 = r^3

27,608.4 ÷ 12.56 = r^3

2,198.12 = r^3

r = 13

Now the area of the cross section is

= πr^2

= 3.14 × (13)^2

= 530.66

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x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2   = -20

divide by -2 on each side

-2x^2   /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15