Surface Areas And Volumes Class 10 Notes Maths: Chapter 13

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Surface Areasand Volumes

Cuboid : In a cuboid, let l be the length, b be the breadth and h be the height, then
(i) Total surface area = 2(lb + bh + lh) sq. units
(ii) Volume = l × b × h cubic unitsunits
(iii) Diagonal of a cuboid =√(l²+b²+h²)units
(iv) Area of the four walls = 2(l+b)h sq. units1

Cube :If the side of a cube is‘a’ units, then
(i) Total surface area = 6a² sq. units
(ii) Volume = a³ cubic units
(iii) Diagonal of a cube = 3a units

Right-Circular Cylinder : For a right-circular cylinder of base r and height h,
(i) Area of each end = πr² sq. units
(ii) Curved surface area = 2πrh sq. units
(iii) Total surface area = 2πr(h+r) sq. units
(iv) Volume = πr²h cubic units

Hollow Cylinder : Let R and r be the external radius and the internal radius, respectively and h be the height of hollow cylinder, then
(i) Area of each end = π(R² – r²) sq. units
(ii) Curved surface area = 2π(R + r)h sq. units
(iii) Total surface area = 2π(R + r)(R + h – r)sq. units
(iv) Volume = π(R² – r²)h cubic units

Right-Circular Cone : If r, h and l denote the radius of the base, height and slant height of a cone, respectively, then
(i) l² = r² + h²
(ii) Curved surface area = πrl sq. units
(iii) Total surface area = πr² + πrl sq. units
(iv) Volume = πr²h cubic units

Sphere : For a sphere of radius r,
(i) Surface area = 4πr² sq. units
(ii) Volume = πr³ cubic units

Hemisphere :For a hemisphere of radius r,
(i) Curved surface area = 2πr² sq. units
(ii) Total surface area = 3πr² sq. units
(iii) Volume = πr³ cubic units

Spherical Shell : For a spherical shell of outer radius R and inner radius r,
(i) Surface area = 4π(R² – r²) sq. units
(ii) Volume of material = π(R³ – r³) cubic units

Frustum of a Cone : If h, l, r1 and r2 denote the height, slant height and radii of the bases of a frustum of a cone, respectively, then
(i) Volume = (r1² + r1r2 + r2²) h cubic units
(ii) Lateral surface area = π(r1 + r2) l sq. units
(iii) Total surface area = π{(r1 + r2)l + (r1² + r2²)} sq. units
(iv) Slant height of the frustum =√(h²+(r1– r2)²) 2
(v) Height of the cone of which the frustum is a part =hr1/(r1-r1)
(vi) Slant height of the cone of which the frustum is a part =hr1/(r1-r1)