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emmainna [20.7K]
3 years ago
6

A cube fits perfectly in a sphere. If the cube has a side length of 10cm, what is the volume of the sphere? Round your answer to

the nearest hundredth (2 decimal places) or leave your answer in Pi form
Mathematics
1 answer:
Goryan [66]3 years ago
3 0

Answer:

Step-by-step explanation:

Since the cube fits perfectly in the sphere, it means that the diagonal of the cube will form the diameter of the sphere. In a cube, all sides are equal. To determine the length of its diagonal, d, we would apply Pythagoras theorem which is expressed as

Hypotenuse² = opposite side² + adjacent side²

Therefore,

d² = 10² + 10² = 200

d = √200 = 14.14cm

Formula for finding the volume of a sphere is expressed as

Volume = 4/3 × π × r³

Radius of sphere = diameter/2 = 14.14/2 = 7.07cm

Volume = 4/3 × π × 7.07³ = 471.19π cm³

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59 points!!!!!!!
MariettaO [177]
A=a+b
2h use this method when you do? - 14a + 200b + 16h = 1712
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Which of the following is not a Pythagorean triple?
Ierofanga [76]

Answer:

  (7, 24, 26)

Step-by-step explanation:

A Pythagorean triple must have an odd number of even numbers. The triple (7, 24, 26) is not a Pythagorean triple.

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<em>Additional comment</em>

For an odd integer n, a triple can be formed as ...

  (n, (n²-1)/2, (n²+1)/2)

That is, the following will be Pythagorean triples.

  • (3, 4, 5)
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Another series involves even numbers and numbers separated by 2:

  (2n, n²-1, n²+1)

  • (8, 15, 17)
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  • (16, 63, 65)

In this list, if n is not a multiple of 2, the triple will be a multiple of one from the odd-number series.

It is a good idea to remember a few of these, as they tend to show up in Algebra, Geometry, and Trigonometry problems.

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For this case we have that the point-slope equation of a line is given by:

(y-y_ {0}) = m (x-x_ {0})

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