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Geometry
> Surface Area of a Sphere
Surface Area of a Sphere
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A
sphere
is a threedimensional space, such as the shape of a football. A sphere is a body bounded by a surface whose every point is equidistant (i.e. the same distance) from a fixed point, called the centre or the origin of the sphere.
Like a circle in three dimensions, all points from the center are constant. The distance from the center to any points on boundary is known as the
radius
of the sphere. The maximum straight distance through the sphere is known as the
diameter
of the sphere. Onehalf of a sphere is called a hemisphere.
We can find the total surface area of a sphere by using the following formula:
SA = 4 π r
^{2}
where r is the radius.
NOTE: The value of
π
can never be calculated exactly, so the surface area of a sphere is only a approximation.
Surface area of sphere in terms of diameter =
πd
^{2}
where d is the diameter of the sphere.
Example 1
: What is the total surface area of a sphere whose radius is 5.5 meters?
Solution:
Given that:
r =5.5
Surface area of the sphere:
SA = 4
×
π
×
r
^{2}
SA
= 4 × π × (5.5)
^{2}
SA
= 4 × 3.14 × 30.25
SA
= 379.94
Thus the surface area of the sphere is 379.94 m
^{2}
.
Example 2
: A spherical ball has a surface area of 2464 cm
^{2}
. Find the radius of the ball, correct to 2 decimal places, using π = 3.142.
Solution:
SA = 4
×
π
×
r
^{2}
In order to find r, we need to isolate it from the equation above:
r
^{2}
= SA / (4π)
r
^{2}
=2464 / (4
×
π)
r
^{2}
=196.054
r = √(196.054)
r = 14.00 cm
Example 3
: Find the surface area of the sphere whose radius is 18 cm. [
π = 3.14
]
Solution:
r = 18 cm
The surface area of a sphere is given by:
SA = 4
×
π
×
r
^{2}
SA = 4
×
π
×
18
^{2}
SA = 4
×
π
×
342
SA = 4069.44 cm
^{2}
The surface area of the sphere is 4069.44 cm2.
Example 4
: Find the surface area of a sphere, whose radius is given as r = 11 cm.
Solution:
The formula for calculating the surface area of sphere is given by:
SA = 4
×
π
×
r
^{2}
SA = 4 × 3.14 × 11
^{2}
SA = 1519.76
The surface area of sphere is 1519.76 cm
^{2}
.
Example 5
: A hemisphere has the radius measured to 8.3 cm. Find the surface area of it without the base.
Solution:
r = 8.3 cm
The surface area of a hemisphere without the base is determined by using the following formula:
SA = 2
×
π
×
r
^{2}
SA = 2
×
π
×
8.3
^{2}
SA = 432.62
The surface area of the hemisphere is therefore 432.62 cm
^{2}
.
Example 6
: Find the surface area of a sphere whose radius is 6cm?
Solution:
SA = 4
×
π
×
r
^{2}
SA = 4
×
π
×
6
^{2}
SA = 4
×
π
×
36
SA = 452cm
^{2}
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