Surface Areas And Volumes Class 10 Notes Maths: Chapter 13

Basic Concepts-01
Chap 13-01

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 ร— b ร— h cubic unitsunits
    (iii) Diagonal of a cuboid =โˆš(l2+b2+h2)units
    (iv) Area of the four walls = 2(l+b)h sq. units1
  • Cube :If the side of a cube isโ€˜aโ€™ 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 = ฯ€r2 sq. units
    (ii) Curved surface area = 2ฯ€rh sq. units
    (iii) Total surface area = 2ฯ€r(h+r) sq. units
    (iv) Volume = ฯ€r2h 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 = ฯ€(R2 โ€“ r2) sq. units
    (ii) Curved surface area = 2ฯ€(R + r)h sq. units
    (iii) Total surface area = 2ฯ€(R + r)(R + h โ€“ r)sq. units
    (iv) Volume = ฯ€(R2 โ€“ 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 = ฯ€rl sq. units
    (iii) Total surface area = ฯ€r2 + ฯ€rl sq. units
    (iv) Volume = ฯ€r2h cubic units
  • Sphere : For a sphere of radius r,
    (i) Surface area = 4ฯ€r2 sq. units
    (ii) Volume = ฯ€r3 cubic units
  • Hemisphere :For a hemisphere of radius r,
    (i) Curved surface area = 2ฯ€r2 sq. units
    (ii) Total surface area = 3ฯ€r2 sq. units
    (iii) Volume = ฯ€r3 cubic units
  • Spherical Shell : For a spherical shell of outer radius R and inner radius r,
    (i) Surface area = 4ฯ€(R2 โ€“ r2) sq. units
    (ii) Volume of material = ฯ€(R3 โ€“ 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 = ฯ€(r1 + r2) l sq. units
    (iii) Total surface area = ฯ€{(r1 + r2)l + (r12 + r22)} sq. units
    (iv) Slant height of the frustum =โˆš(h2+(r1โ€“ 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)