The curved surface area (CSA) of a sphere is the same as its total surface area because it is a single, continuous, and perfectly symmetrical curved surface with no flat faces or edges. Vedantu +1
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.
A sphere has a curved surface area only. All of the sphere surface points are equally far from the center. An object that certainly has flat faces is a polyhedron. The sphere is not a polyhedron since the vertices, edges, and flat surfaces are not present.
For a sphere, the Total Surface Area (TSA) and the Curved Surface Area (CSA) are the same because a sphere has no edges or flat faces. Both are calculated using the formula 4πr².
Curved Surface Area- The curved surface area is defined as the area of only curved surface, leaving the circular top and base. Total Surface Area- It is the area of the curved surface as well as the bases.
Hence, the volume of a cuboid, V = l × b × h = lbh units3, where 'l' 'b' and 'h' represent the length, breadth, and height of the cuboid.
TSA is used to determine the amount of material needed to make a cylindrical container. CSA is used to determine the amount of wrapping paper needed to wrap a cylindrical gift.
(You can find out d is 2 times of the r.) To understand the circumference C , imagine "unrolling " C into a straight line. The formula for the circumference is C= 3.14d=3.14*2*r.
The curved surface area can easily be calculated by the multiplication of the base radius, pi, and slant height. It is calculated in square units.
Answer: The statement is true.
Spherical Curve. A curve on the surface of a sphere. Examples include the baseball cover, Seiffert's spherical spiral, spherical helix, and spherical spiral.
Curved Surface Area (CSA) – It includes the area of all the curved surfaces. Lateral Surface Area (LSA) – It includes the area of all the surface excluding the top and bottom areas. Total Surface Area (TSA) – It includes the area of all the surfaces of the object including the bases.
I see that f(u)=acos(u) and g(u)=asin(u). I have been given that the Gaussian curvature can be calculated by K=−f″(u)f(u) and the mean curvature by H=12(g′(u)f(u)−f″(u)g′(u)) (with ′ meaning differentiation with respect to u).
The surface area of a sphere represents the total area covered by its curved surface. To calculate the surface area, we use the standard formula: 4πr², where π (pi) is a mathematical constant approximately equal to 3.14159, and r represents the radius of the sphere.
CSA stands for Curved Surface Area ( 2 π r h ), which covers the side of the cylinder only. TSA means Total Surface Area ( 2 π r ( r + h ) ), which includes the side and both circular bases. The formula π d l calculates the curved surface area of a cylinder, where d is the diameter and l is the height.
Curved Surface Area of Sphere
The curved surface area is the sum of areas of all the curved regions of the solid. CSA of a sphere = 4 π r 2 , where “r” is the sphere's radius.
For a sphere, the Total Surface Area (TSA) is the surface area of the entire sphere. The Curved Surface Area (CSA) of a sphere is the same as the TSA because a sphere has no flat surfaces.
TSA (Total Surface Area) includes all cylinder surfaces using formula 2πr² + 2πrh, while CSA (Curved Surface Area) only covers the lateral surface using formula 2πrh.
We cannot be 100% sure that a mathematical theorem holds; we just have good reasons to believe it. As any other science, mathematics is based on belief that its results are correct.
Volume of a cuboid = l × b × h [cubic units]
Where, l = length. b = breadth. h = height.