class 10 maths chapter 13 surface areas and volumes

CUBOID

1. Surface area of cuboid= 2(lb + bh +hl) sq. units
2. Volume of Cuboid = lbh cubic units

CUBE

1. Surface area of cube = 6s² sq. units
2. Volume of cube = s³ cubic units

CYLINDER

1. Curved surface area of cylinder of radius r and height h = 2πrh square units.
2. Total surface area of cylinder of radius r and height h = 2πr (r + h) square units.
3. Volume of cylinder of radius r and height h = πr²h cubic units.

CONE

1. Curved surface area of cone of radius r, height h and slant height l = πrl square units where l= √ r² +h²
2. Total surface area of cone of radius r, slant height l = πr (l +r) sq. units.
3. Volume of cone of radius r, height h =¹/₃ πr²h cubic units.

SPHERE

1. Total surface area of sphere of radius r units = 4πr² sq. units.
2. Volume of sphere of radius r units = 4/3πr3 cubic units.

HEMISPHERE

1. Curved surface area of hemisphere of radius r units = 2πr²sq. units.
2. Total surface area of a solid hemisphere of radius r units = 3πr² sq. units.
3. Volume of hemisphere of radius r units =²/₃πr³ cubic units.

FRUSTUM

1. Curved surface area of frustum = πl(r + R) sq. units. Where l slant height of frustum and radii of circular ends are r and R.
2. Total surface area of frustum = πl(r+ R) +π(r² + R²) sq. units.
3. Volume of Frustum =¹/₃πh(r²+ R² + rR) cubic units.
4. l= √h²+(R-r)² units