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stira [4]
3 years ago
7

A sphere has a volume of 36π m3. Find the surface area of the sphere.

Mathematics
1 answer:
shusha [124]3 years ago
5 0
V=4/3πr^3
36π=4/3πr^3
3/4(36π)=(4/3πr^3)3/4
27π=πr^3
π(27π)=r^3
27=r^3
square root
r=3
s.a=4πr^2
s.a=4π(3^2)
s.a=4π(9)
s.a=36π
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Phoenix [80]

So for this, we will be applying the Triangle Inequality Theorem, which states that the sum of 2 sides must be greater than the third side for it to be a triangle. If any inequality turns out to be false, then the set cannot be a triangle.

A+B>C\\A+C>B\\B+C>A

<h2>First Option: {6, 10, 12}</h2>

Let A = 6, B = 10, and C = 12:

6+10>12\\16>12\ \textsf{true}\\\\6+12>10\\18>10\ \textsf{true}\\\\12+10>6\\22>6\ \textsf{true}

<h2>Second Option: {5, 7, 10}</h2>

Let A = 5, B = 7, and C = 10

5+7>10\\12>10\ \textsf{true}\\\\5+10>7\\15>7\ \textsf{true}\\\\10+7>5\\17>5\ \textsf{true}

<h2>Third Option: {4, 4, 9}</h2>

Let A = 4, B = 4, and C = 9

4+4>9\\8>9\ \textsf{false}\\\\4+9>4\\13>4\ \textsf{true}\\\\4+9>4\\13>4\ \textsf{true}

<h2>Fourth Option: {2, 3, 3}</h2>

Let A = 2, B = 3, and C = 3

2+3>3\\5>3\ \textsf{true}\\\\2+3>3\\5>3\ \textsf{true}\\\\3+3>2\\6>2\ \textsf{true}

<h2>Conclusion:</h2>

Since the third option had an inequality that was false, <u>the third option cannot be a triangle.</u>

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\boxed{y+5=-5x-5}

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