What are the cross sections of a sphere?
Table of Contents
The intersection of a plane figure with a sphere is a circle. All cross-sections of a sphere are circles.
What is the shape of a cross section formed that is perpendicular to the base of a cylinder?
rectangular shape
The cross-section perpendicular to the base of a cylinder given as a rectangular shape.
Can a sphere have a cross section that is a point?
Of all shapes, a sphere has the smallest surface area for its volume….
| • | Spheres are perfectly round geometric objects. |
|---|---|
| • | The intersection of a plane with a sphere is a circle (or a point if tangent to sphere). |
| • | All cross sections of a sphere are circles. (All circles are similar to one another.) |
How many circles make a sphere?
A sphere is the set of all points, in three-dimensional space, which are equidistant from a point. You can think of a sphere as a three-dimensional circle.
How many curved surfaces does a sphere have?
1 curved surface
Spheres: • are perfectly round: • have no edges; • have no vertices; • have 1 curved surface.
What is the curved surface area of a sphere?
4πr²
Since the sphere is a complete curved shape therefore the curved surface area is equal to the total area of sphere. It is also called lateral surface area. Surface Area of Sphere = 4πr², where r is the radius of sphere.
What is the shape of a cross section that is perpendicular to the base of a triangular prism?
rectangle
SOLUTION: A plane perpendicular to the bases will intersect both bases on a straight line and the curved edge on two parallel lines. The resulting cross section is a rectangle. SOLUTION: A plane parallel to the base of a triangular prism will intersect a cross section that is the same shape as its bases.
What is the perpendicular cross section of a cone?
Perpendicular Cross Section of a Cone. When a plane passes through a cone to create a cross section that is perpendicular to the base and whose base is the diameter of the cone, it will result in a triangle.
What is a perpendicular cross section of a pyramid?
Cross sections perpendicular to the base and through the vertex will be triangles. Below, you can see a plane cutting through the pyramid, part of the pyramid removed, and the cross section. You could also take a slice parallel to the base. Cross sections parallel to the base will be hexagons.
What is the shape of sphere?
What is a Sphere? A sphere is a perfectly-round 3D shape in the shape of a ball. All the points of its surface are equidistant (an equal distance) from its centre, meaning that it is smooth and has no edges or vertices.
How many faces has a sphere?
one
A face is a flat or curved surface on a 3D shape. For example a cube has six faces, a cylinder has three and a sphere has just one.
How many curved lines does a circle have?
one curved side
In our primary education resources, we say that a circle has one curved side.
What is a perpendicular cross-section?
In perpendicular cross-section, a plane cuts the solid shape in the vertical direction (i.e., perpendicular to the base) such that it creates a perpendicular cross-section The cross sectional area of different solids is given here with examples.
What is the size of the cross section of a sphere?
The size of the cross section may vary depending on the point of intersection of plane and sphere. If the plane passed through the center of sphere, then it divides the sphere into two equal parts (i.e. hemisphere). How does the cross section of cone looks like?
What is the shape of the cross section of a prism?
Remember, perpendicular lines intersect the base at ninety degrees. Again, the cross-section is shaped like a rectangle. However, this time it has the same shape and size as another face of the prism. Think about slicing the prism with a plane tilted away from its base.
How is the oval shape of a sphere obtained?
The oval shape is obtained when the plane cuts the cylinder parallel to the base with slight variation in its angle We know that of all the shapes, a sphere has the smallest surface area for its volume. The intersection of a plane figure with a sphere is a circle. All cross-sections of a sphere are circles.