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05 Feb 2022, 07:45
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Having present hemisphere is half of a sphere.
If we inscribe a circular cone in a hemisphere, the base of the cone must coincide with the base of the hemisphere, both are identical circumferences.
Thus the radius of the base of the circular cone is the same radius as the base of the hemisphere.
Since the hemisphere is half that of a sphere, the height of the sphere coincides with the height of the cone.
The height of the sphere is the radius of the base of the hemisphere.
Therefore, the radius of the sphere is equal to the height of the cone with a circular base.
Answer B
If we inscribe a circular cone in a hemisphere, the base of the cone must coincide with the base of the hemisphere, both are identical circumferences.
Thus the radius of the base of the circular cone is the same radius as the base of the hemisphere.
Since the hemisphere is half that of a sphere, the height of the sphere coincides with the height of the cone.
The height of the sphere is the radius of the base of the hemisphere.
Therefore, the radius of the sphere is equal to the height of the cone with a circular base.
Answer B
03 Nov 2022, 06:25
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Bunuel
A question. If the cone is right circular one, shouldn't the triangle shown above be equilateral with 60 degrees each? That is why I thought it would be a 90-60-30 triangle. Someone please help.
03 Jun 2023, 07:32
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Let's consider the given scenario: a right circular cone inscribed in a hemisphere, with the base of the cone coinciding with the base of the hemisphere.
To find the ratio of the height of the cone to the radius of the hemisphere, let's denote the height of the cone as h and the radius of the hemisphere as r.
The radius of the hemisphere is the same as the radius of the cone, since the base of the cone coincides with the base of the hemisphere.
Let's draw a line connecting the apex of the cone to the center of the base of the hemisphere. This line will be the height of the cone.
We can observe that the line connecting the apex of the cone to the center of the base of the hemisphere is also the radius of the hemisphere. Therefore, the radius r of the hemisphere is equal to the height h of the cone.
Now, the ratio of the height of the cone to the radius of the hemisphere is h:r, which is equal to h/h.
This simplifies to 1:1.
Therefore, the ratio of the height of the cone to the radius of the hemisphere is (B) 1:1.
To find the ratio of the height of the cone to the radius of the hemisphere, let's denote the height of the cone as h and the radius of the hemisphere as r.
The radius of the hemisphere is the same as the radius of the cone, since the base of the cone coincides with the base of the hemisphere.
Let's draw a line connecting the apex of the cone to the center of the base of the hemisphere. This line will be the height of the cone.
We can observe that the line connecting the apex of the cone to the center of the base of the hemisphere is also the radius of the hemisphere. Therefore, the radius r of the hemisphere is equal to the height h of the cone.
Now, the ratio of the height of the cone to the radius of the hemisphere is h:r, which is equal to h/h.
This simplifies to 1:1.
Therefore, the ratio of the height of the cone to the radius of the hemisphere is (B) 1:1.
