write all formulas of chapter 13 class 10
Answers
Answer:
subject kya hai
Step-by-step explanation:
state board or cbsc
CUBOID:
Cuboid with length l, breadth b and height h
The total surface area of the cuboid(TSA) = Sum of the areas of all its six faces
TSA (cuboid) = 2(l×b)+2(b×h)+2(l×h)=2(lb+bh+lh)
Lateral surface area (LSA) is the area of all the sides apart from the top and bottom faces.
The lateral surface area of the cuboid = Area of face AEHD + Area of face BFGC + Area of face ABFE + Area of face DHGC
LSA (cuboid) = 2(b×h)+2(l×h)=2h(l+b)
Length of diagonal of a cuboid =√(l²+b²+h²)
Volume of a cuboid =(base area)×height=(lb)h=lbh
CUBE:
Cube with length l
TSA (cube) =2×(3l²)=6l²
Similarly, the Lateral surface area of cube =2(l×l+l×l)=4l²
Note: Diagonal of a cube =√3l
Volume of a cube = base area×height
Since all dimensions of a cube are identical, volume = l3
Where l is the length of the edge of the cube.
CYLINDER:
Transformation of a Cylinder into a rectangle.
CSA of a cylinder of base radius r and height h=2π×r×h
TSA of a cylinder of base radius r and height h=2π×r×h + area of two circular bases
=2π×r×h+2πr²
=2πr(h+r)
Volume of a cylinder = Base area × its height = (π×r²)×h=πr²h
RIGHT CIRCULAR CONE:
Consider a right circular cone with slant length l, radius r and height h.
Cone with base radius r and height h
CSA of right circular cone =πrl
TSA = CSA + area of base =πrl+πr2=πr(l+r)
The volume of a Right circular cone is 1/3 times that of a cylinder of same height and base.
In other words, 3 cones make a cylinder of the same height and base.
The volume of a Right circular cone =(1/3)πr²h
Where r is the radius of the cone and h is the height of the cone.
SPHERE:
For a sphere of radius r
Curved Surface Area (CSA) = Total Surface Area (TSA) = 4πr²
The volume of a sphere of radius r =(4/3)πr³
HEMISPHERE:
Hemisphere of radius r
We know that the CSA of a sphere =4πr². A hemisphere is half of a sphere.
∴ CSA of a hemisphere of radius r =2πr²
Total Surface Area = curved surface area + area of the base circle
⇒TSA =3πr²
The volume (V) of a hemisphere will be half of that of a sphere.
∴ The volume of the hemisphere of radius r =(2/3)πr³