what do we mean by a hollow sphere and a hemisphere. is it hollow from bothe sides or not. if not then what is it. how did we derived the formula of curved ,total,volume .I am really confused. Please solve my problem and clear my concept ragarding this.Please explain it cleraly and correctly . I will be really thankful to those who will answer it.God bless those people.
2007-12-29 18:34:55 · 3 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
a hollow sphere means that you only take the shell of your object... the inside is hollow...
a hemisphere is half a sphere...
consider the earth (assume its a perfect sphere)
the northern hemisphere is the part above the equator...
the hollow sphere means ... you take the crust part of the earth... and remove the mantle and the cores...
volume of sphere = (4/3) π r^3.. r = radius
§
2007-12-29 18:56:08 · answer #1 · answered by Alam Ko Iyan 7 · 0⤊ 0⤋
A sphere is the locus of points defined by the general equation
(x - a)² + (y - b)² + (z - c)² = r²
where (a, b, c) is the center and r is the radius of the sphere. Passing a plane through the center of the sphere divides the sphere into two equal parts called hemispheres. A solid sphere can be defined by the inequality
(x - a)² + (y - b)² + (z - c)² ⤠r²
and a spherical shell is defined by
(r - d)² ⤠(x - a)² + (y - b)² + (z - c)² ⤠r²
The surface area of a sphere is easily derived in spherical coordinates:
dA = r²sinθdθdФ
dA = 2Ïr²sinθdθ
A = - 2Ïr²(cosÏ - cos0)
A = 4Ïr²
and the volume of a sphere becomes
dV = r²sinθdθdФdr
dV = (1/3)r³sinθdθdФ
dV = (2Ï/3)r³sinθdθ
dV = - (2Ï/3)r³(cosÏ - cos0)
V = (4/3)Ïr³
The surface area and volume of a hemisphere are, of course, half those of a full sphere.
2007-12-30 04:19:11 · answer #2 · answered by Helmut 7 · 0⤊ 0⤋
a hollow sphere is any any normal sphere which is hollow..a hemisphere is the exact half of it..such that if two such pieces held together will make a perfect sphere...
area of a circle is 22/7*square of the radius .
so if we take the diameter of the circle and consider it as its axis and rotate itfirst vir tically and the horizontally, we will get the area of the sphere which is 4 * 22/7*square of the radius..
if we divide this by half we will get the csa of a hemisphere.
2007-12-30 03:00:24 · answer #3 · answered by ani 2 · 0⤊ 0⤋