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This is incorrect. The problem with the answer starts here:
"Also, the point will lie on the plane which divides the top and bottom such that the volumes are equal."
This would only be true if the cg's for both halves were the same distance from that plane. But they aren't.
The solution is pi*int( t*(a2-t2)dt,0 to a)/(volume of hemisphere=2/3*pi*a3)
pi's cancel.
cg at ([a2t2/2-t4/4],0,a)/(2/3*a3)
= (a4/4)/(2/3*a3)
= 3/8 a from the base.
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Whoops! I did not mean to wipe out the original answer, and am a bit surprised that I apparently have the power to do that. Sorry!
The original answer found the distance from the base to a plane that divided the hemisphere into two equal halves, at t= ~0.347a. That might be useful information but is not the cg.
What else can I help you with?
What is a steradian?
A steradian is the solid angle subtended at the centre of a sphere by radius r by a portion of the surface of the sphere which has area r2.
What is a solid half circle called?
hemisphere
If you know the radius of a cross section 8 inches from the center of a circle how do you calculate the radius at the center?
The radius of a circle is constant regardless of where it is, so if the radius of the circle at a cross section is 8 inches, then the radius of the circle is 8 inches. However, if you mean you know the length of the chord 8 inches from the centre of the circle, then you can create an isosceles triangle by joining the ends of the chord to the centre of the circle. If you now drop a perpendicular from the centre of the circle where the radii drawn in meet, it will bisect the chord and form two congruent right triangles which have one leg 8 inches long, one leg half the length of the chord and a hypotenuse the radius of the circle. You can now use Pythagoras to find the unknown radius from the two lengths you do know: radius² = (8 in²) + (chord_length/2)² There is more to this problem which you have not stated as it is very unusual to use the phrase "CROSS-SECTION 8 inches from the centre OF A CIRCLE"; cross-sections are used with 3 dimensional objects whereas a circle is a 2 dimensional object. I would guess that you have some solid (say a sphere) where a circular cross-section has been created 8 inches from the centre of the object and you want to know its radius. In this case you can use Pythagoras as above: radius_object² = (8 in)² + (radius_circle)² by considering a plane that slices through the centre of the original object and bisects the circle created in the cross-section.
What solid figure has two faces but no vertices or edges?
A hemisphere
A solid figure which has both a flat and a curved surface?
A cylinder or a cone. Or a hemisphere.
What is the Moment of inertia of a solid hemisphere?
The moment of inertia of a solid hemisphere rotating around its axis is given by (2/5) * m * r^2, where m is the mass of the hemisphere and r is the radius.
Definition of solid angle?
solid angle is the ratio of the intercepted area dA of the spherical surface , described about the apex O as the centre ,to square of its radius r
How can you find center of mass of solid hemisphere?
To find the center of mass of a solid hemisphere, you can divide it into elementary components, such as disks or cylindrical shells, and integrate their individual masses over the hemisphere's volume. By dividing the mass-weighted points by the total mass, you can determine the coordinates of the center of mass in three dimensions.
What is total surface area of solid hemisphere of radius r?
It is in square units: (2*pi*radius2)+(pi*radius2)
What is a steradian?
A steradian is the solid angle subtended at the centre of a sphere by radius r by a portion of the surface of the sphere which has area r2.
Which place is Center of the Earth?
The centre of the earth is solid iron, however the centre of the earths gravitational pull changes, due to the movement of the moon, which has an effect on the earths gravity.
What is a solid half circle called?
hemisphere
How many edges does a solid hemisphere have?
One.
Two unequal masses are attached to the ends of a solid rod. which mass is nearest to the Centre of Mass lighter or heavier?
The heavier mass will be nearest to the center of mass. The concept behind this is related to the one that explains the center of gravity. The center of mass and the center of gravity are the same.
How can gravity affect a solid rock?
gravity affects everything with mass
Is center of gravity lies where there is no mass?
That all depends on the shape of the object and how its mass is distributed. The center of gravity of a solid sphere is at the center of the solid sphere. The center of gravity of a solid cube is at the center of the solid cube. The Earth's center of gravity is at the center of the Earth, and there's certainly plenty of mass there. But the center of gravity of a ring is at the center of the ring ... an open space where the finger goes.
What is the motto of Gravity Technologies?
Gravity Technologies's motto is 'Rock solid recommendations.'.
