Class 8 Maths Mensuration Notes & MCQs

Class 8 Maths Mensuration Notes & MCQs

Mensuration – Quick Notes (Class 8 NCERT)

Definition:

Mensuration deals with measuring lengths, areas, and volumes of geometrical shapes and solids.

  • Applications: Area of land, surface area of solids, volume of containers, etc.

1. Surface Area (SA) of 3D Shapes

ShapeSurface Area Formula
CubeSA=6a2SA = 6a^2SA=6a2
CuboidSA=2(lb+bh+hl)SA = 2(lb + bh + hl)SA=2(lb+bh+hl)
SphereSA=4πr2SA = 4\pi r^2SA=4πr2
HemisphereSA=3πr2SA = 3\pi r^2SA=3πr2
CylinderSA=2πr(h+r)SA = 2\pi r(h + r)SA=2πr(h+r)
ConeSA=πr(l+r)SA = \pi r(l + r)SA=πr(l+r), l=slant heightl = \text{slant height}l=slant height

2. Volume of 3D Shapes

ShapeVolume Formula
CubeV=a3V = a^3V=a3
CuboidV=l⋅b⋅hV = l \cdot b \cdot hV=l⋅b⋅h
SphereV=43πr3V = \frac{4}{3}\pi r^3V=34​πr3
HemisphereV=23πr3V = \frac{2}{3}\pi r^3V=32​πr3
CylinderV=πr2hV = \pi r^2 hV=πr2h
ConeV=13πr2hV = \frac{1}{3}\pi r^2 hV=31​πr2h

3. Important Notes / Tips

  • Slant height of a cone: l=r2+h2l = \sqrt{r^2 + h^2}l=r2+h2​
  • SA of hemisphere includes curved + base: 3πr23\pi r^23πr2
  • Cylinder SA includes 2 circular ends + curved surface: 2πr(h+r)2\pi r(h + r)2πr(h+r)
  • Volume = area of base × height for prism-like solids
  • Use π ≈ 3.14 or 22/7 depending on the problem

Mensuration – MCQ Q&A

  1. Q: Surface area of a cube with side 5 cm?
    A: 6×52=150 cm26 × 5^2 = 150\ cm^26×52=150 cm2
  2. Q: Volume of a cube with side 3 cm?
    A: 33=27 cm33^3 = 27\ cm^333=27 cm3
  3. Q: Surface area of a cuboid 2×3×4 cm?
    A: 2(lb+bh+hl)=2(2×3+3×4+4×2)=52 cm22(lb + bh + hl) = 2(2×3 + 3×4 + 4×2) = 52\ cm^22(lb+bh+hl)=2(2×3+3×4+4×2)=52 cm2
  4. Q: Volume of cuboid 2×3×4 cm?
    A: V=2×3×4=24 cm3V = 2×3×4 = 24\ cm^3V=2×3×4=24 cm3
  5. Q: SA of sphere radius 7 cm?
    A: 4πr2=4×3.14×72≈615.44 cm24π r^2 = 4 × 3.14 × 7^2 ≈ 615.44\ cm^24πr2=4×3.14×72≈615.44 cm2
  6. Q: Volume of sphere radius 7 cm?
    A: V=4/3πr3≈1436.03 cm3V = 4/3 π r^3 ≈ 1436.03\ cm^3V=4/3πr3≈1436.03 cm3
  7. Q: SA of cylinder radius 3 cm, height 10 cm?
    A: 2πr(h+r)=2×3.14×3(10+3)≈245.64 cm22π r(h + r) = 2 × 3.14 × 3(10 + 3) ≈ 245.64\ cm^22πr(h+r)=2×3.14×3(10+3)≈245.64 cm2
  8. Q: Volume of cylinder radius 3 cm, height 10 cm?
    A: πr2h=3.14×9×10≈282.6 cm3π r^2 h = 3.14 × 9 × 10 ≈ 282.6\ cm^3πr2h=3.14×9×10≈282.6 cm3
  9. Q: SA of cone radius 4 cm, slant height 5 cm?
    A: πr(l+r)=3.14×4(5+4)≈113.04 cm2π r(l + r) = 3.14 × 4(5 + 4) ≈ 113.04\ cm^2πr(l+r)=3.14×4(5+4)≈113.04 cm2
  10. Q: Volume of cone radius 4 cm, height 3 cm?
    A: V=1/3πr2h=1/3×3.14×16×3≈50.24 cm3V = 1/3 π r^2 h = 1/3 × 3.14 × 16 × 3 ≈ 50.24\ cm^3V=1/3πr2h=1/3×3.14×16×3≈50.24 cm3
  11. Q: SA of hemisphere radius 7 cm?
    A: 3πr2=3×3.14×49≈461.58 cm23π r^2 = 3 × 3.14 × 49 ≈ 461.58\ cm^23πr2=3×3.14×49≈461.58 cm2
  12. Q: Volume of hemisphere radius 7 cm?
    A: 2/3πr3≈717.56 cm32/3 π r^3 ≈ 717.56\ cm^32/3πr3≈717.56 cm3
  13. Q: Slant height formula for cone?
    A: l=r2+h2l = \sqrt{r^2 + h^2}l=r2+h2​
  14. Q: Curved surface area (CSA) of cylinder?
    A: 2πrh2π r h2πrh
  15. Q: Curved surface area of cone?
    A: πrlπ r lπrl
  16. Q: Volume formula for prism-like solid?
    A: Area of base × height ✅
  17. Q: Cube side 10 cm → Volume?
    A: 103=1000 cm310^3 = 1000\ cm^3103=1000 cm3
  18. Q: Cylinder radius 7 cm, height 14 cm → Volume?
    A: πr2h=3.14×49×14≈2152.36 cm3π r^2 h = 3.14 × 49 × 14 ≈ 2152.36\ cm^3πr2h=3.14×49×14≈2152.36 cm3
  19. Q: Sphere radius 21 cm → Volume?
    A: 4/3πr3=4/3×3.14×9261≈38777.68 cm34/3 π r^3 = 4/3 × 3.14 × 9261 ≈ 38777.68\ cm^34/3πr3=4/3×3.14×9261≈38777.68 cm3
  20. Q: Cube side 6 cm → SA?
    A: 6×62=216 cm26 × 6^2 = 216\ cm^26×62=216 cm2