The perimeter of the largest cross section of a sphere is 88 centimeters.
2 answers:
Answer:
Radius of the sphere is 14 cm and Volume of the sphere is 1498.7 cm³.
Step-by-step explanation:
Given Perimeter of the largest cross section of the sphere = 88 cm.
We have to find Radius of the sphere and Volume of the sphere.
We know that Largest Cross section of the sphere is a circle whose radius is same as of sphere.
let r be the radius of cross sectional circle or sphere.
Now,
Circumference of circle = 88 cm
2πr = 88
r = 2 × 7
r = 14 cm
Volume of the sphere =
=
=
= 11498.7 cm³
Therefore, Radius of the sphere is 14 cm and Volume of the sphere is 1498.7 cm³.
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You haven't provided the series, therefore, I can only help with the concept.
<u><em>For an infinite geometric series, we have two possibilities for the common ratio (r):</em></u>
for r > 1, the terms in the series will keep increasing infinitely and the only possible logic summation of the series would be infinity
for r < 1, the terms will decrease, therefore, we can formulate a rule to get the sum of the infinite series
<u><em>In an infinite series with r < 1, the summation can be found using the following rule:</em></u>
sum =
where:
a₁ is the first term in the series
r is the common ratio
<u>Example:</u>
For the series:
2 , 1, 0.5 , 0.25 , ....
we have:
a₁ = 2
r = 0.5
Therefre:
sum =
Hope this helps :)
<u><em>For an infinite geometric series, we have two possibilities for the common ratio (r):</em></u>
for r > 1, the terms in the series will keep increasing infinitely and the only possible logic summation of the series would be infinity
for r < 1, the terms will decrease, therefore, we can formulate a rule to get the sum of the infinite series
<u><em>In an infinite series with r < 1, the summation can be found using the following rule:</em></u>
sum =
where:
a₁ is the first term in the series
r is the common ratio
<u>Example:</u>
For the series:
2 , 1, 0.5 , 0.25 , ....
we have:
a₁ = 2
r = 0.5
Therefre:
sum =
Hope this helps :)