2 years ago

The surface area of a ball is 3,600 square millimeters. What is the balls radius

1 answer:

4 0

$A = 4 \pi r^2$

$3600 = 4\pi r^2$

$\dfrac{3600}{4 \pi} = r^2$

$r^2 = 286.479$

$r = 16.9$

Answer: The radius is 16.9 mm.

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Nesterboy [21]

Answer: $230^{\circ$

Step-by-step explanation:

For convenience, I labeled some points as shown in the attached picture.

Also, I assume $\overline{AB}$ and $\overline{BC}$ are tangents to the circle.

$\overline{BO} \cong \overline{BO}$ (reflexive property)
$\overline{AB} \cong \overline{BC}$ (tangents drawn from a common external point are congruent)
$\angle BAO \cong \angle BCO$ (right angles are congruent)

Therefore, we know $\triangle ABO \cong \triangle CBO$ by HL.

Thus, by CPCTC,

$\angle AOB \cong \angle BOC \implies m\angle BOC=65^{\circ}\\\\\implies m\angle AOC=130^{\circ}$

This means the measure of minor arc AC is $130^{\circ}$ , and thus $b=360^{\circ}-130^{\circ}=\boxed{230^{\circ}}$

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