SOLUTION: The ratio of the altitude of a zone to the diameter of the sphere on which it is 1:5. The area of the zone is 80 pi. Find the area of the sphere.
Algebra.Com
Question 1203307: The ratio of the altitude of a zone to the diameter of the sphere on which it is 1:5. The area of the zone is 80 pi. Find the area of the sphere.
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20849) (Show Source): You can put this solution on YOUR website!
Surface area of a sphere:
let altitude be and diameter
given ratio is
so,
=>
The area of a spherical zone can be calculated using the formula
where is the height of the spherical layer and is the radius of the sphere.
if the area of the zone is , we have
...simplify
.....substitute
then, surface area of a sphere is:
Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
.
The solution by @MathLover1 is incorrect.
I came to bring you a correct solution.
Surface area of a sphere:
let altitude be and diameter
given ratio is
so,
--> <<<---=== it is where @MathLover1 made her mistake.
The area of a spherical zone can be calculated using the formula
where is the height of the spherical zone and is the radius of the sphere.
if the area of the spherical zone is , we have
...simplify
.....substitute
then, surface area of a sphere is:
ANSWER
Solved (correctly).
RELATED QUESTIONS
the ratio of the altitude of a zone to the diameter of the sphere on which it is 1:5. the (answered by MathLover1,ikleyn)
The area of a zone is 50.265 sq. cm. if the altitude of the zone is 2 cm, solve the... (answered by math_tutor2020)
The area of a zone is 50.265 sq.cm. If the altitude of the zone is 2 cm, solve the... (answered by MathLover1)
SOLID MENSURATION:the area of a zone of altitude 4 cm is equal to the area of the lune... (answered by Alan3354)
The altitude of a zone is 2 cm and the radius of the sphere is 9 cm. Find the volume of... (answered by CPhill)
Find the volume of a spherical sector of a sphere whose surface area is 437π m^2, if (answered by Alex.33)
A sphere segment has a volume of 904.78 cu.cm.If the radius of the sphere is 10cm, solve... (answered by math_helper)
On a sphere of diameter 125cm, two circles of the sphere whose planes are parallel have a (answered by Edwin McCravy,ikleyn)
A spherical segment has a volume of 904.78 . if the radius of the sphere is 10 , solve... (answered by Theo,ikleyn)