Is surface area of a sphere is equal to CSA of the circumscribed cylinder justify your answer?

Sol: Let the radius of the sphere = rSurface area of the sphere = 4πr2 Radius of the cylinder circumscribed over the sphere = r Height of the cylinder circumscribed over the sphere (h) = 2rCurved surface area of the cylinder = 2πrh = 2πr(2r) = 4πr2Therefore, the curved surface area of the circumscribed cylinder over a …

How does the surface area of a sphere compare to the surface area of a cylinder in which it fits perfectly?

The sphere of radius has surface area . If the sphere fits perfectly inside the cylinder then the cylinder has radius . If the cylinder does not have a closing top and bottom then the surface area of the cylinder is where is the height of the cylinder.

What is the lateral surface area of a sphere?

The lateral surface area of a sphere is given by 4πr2 4 π r 2 where r is the radius of the sphere. Hence, the Curved Surface Area (CSA) of a Hemisphere is given by 2πr2 2 π r 2 where r is the radius of the sphere of which the hemisphere is a part. The total surface area (TSA) of a Hemisphere is given by 3πr2.

What is the relationship between the volume of a sphere and the volume of a cylinder?

What is the relationship between the volume of the sphere and the volume of the cylinder? (Answer: The sphere takes up two-thirds of the volume of the cylinder.)

What is circumscribed cylinder?

The Sphere and Cylinder The ratio of the volume of a sphere is two-thirds the volume of a circumscribed cylinder (Circumscribed refers to a shape surrounding another shape. Inscribed refers to a shape inside another shape).

Why is the surface area of a sphere?

The Greek mathematician Archimedes discovered that the surface area of a sphere is the same as the lateral surface area of a cylinder having the same radius as the sphere and a height the length of the diameter of the sphere. The lateral surface area of the cylinder is 2πrh where h=2r .

Is lateral area the same as surface area?

The total surface area of a solid is the sum of the areas of all of the faces or surfaces that enclose the solid. The faces include the tops and bottoms (bases) and the remaining surfaces. The lateral surface area of a solid is the surface area of the solid without the bases.

How does the volume of the sphere compared to the cone?

The formula for the volume of a sphere is 4⁄3πr³. A cone is ⅓ the volume of a cylinder, or 1⁄3πr²h.

What is the relationship between sphere and cone?

A right cone is a cone with its vertex directly above the center of its base. has a circular base that is joined to a single point (called the vertex). A sphere is a three-dimensional solid consisting of all points that have the same distance from a given center….Surface Area of a Cone.