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Gyaan Maths
CBSE · Class 6-10
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CBSE Maths · Class 10

Chapter 12: Surface Areas and Volumes

Name: ________________________
Date: ______________
Marks: ____ / 10

Formulas for combinations of solids: cube, cuboid, cylinder, cone, sphere, hemisphere, and frustum.

Questions

  1. TSA of a cube with edge 55.
  2. Volume of cylinder r=7,h=10r = 7, h = 10.
  3. Volume of hemisphere r=7r = 7.
  4. Volume of cone r=6,h=8r = 6, h = 8.
  5. TSA of hemisphere r=7r = 7.
  6. Frustum vol: h=8,r1=5,r2=3h=8, r_1=5, r_2=3.
  7. Sphere of radius 66 melted into cones of r=3,h=4r=3, h=4: number?
  8. A cylinder of radius 22 m and height 1414 m: capacity in litres.
  9. TSA of cuboid l=8,b=6,h=5l=8, b=6, h=5.
  10. A metallic cone of r=6,h=12r = 6, h = 12 is melted into small spherical balls of r=1r = 1. Number of balls?

Extra Practice (Optional)

  • Volume of sphere r=5r = 5.
  • TSA of frustum r1=6,r2=3,h=4r_1 = 6, r_2 = 3, h = 4.
  • Height of a cone if r=3r = 3 and TSA =24π= 24\pi.
  • Ratio of volumes of a cone, hemisphere, cylinder of same base and height.
  • Volume of gladiolus-shape: hemisphere on top of cylinder.

Answer Key (For Teachers)

  1. Answer: 150150.
    Working: 6a26a^2.
  2. Answer: 15401540.
    Working: πr2h\pi r^2 h.
  3. Answer: ≈718.67\approx 718.67.
    Working: 23πr3\tfrac{2}{3}\pi r^3.
  4. Answer: 96π96\pi.
    Working: 13πr2h\tfrac{1}{3}\pi r^2 h.
  5. Answer: 462462.
    Working: 3πr23\pi r^2.
  6. Answer: 392π3\dfrac{392\pi}{3}.
    Working: Formula.
  7. Answer: 2424.
    Working: 288π/12π288\pi/12\pi.
  8. Answer: 176000176000 L.
    Working: π⋅4⋅14=176\pi\cdot 4\cdot 14 = 176 m3=176000^3 = 176000 L.
  9. Answer: 236236.
    Working: 2(lb+bh+hl)=2(48+30+40)2(lb+bh+hl) = 2(48+30+40).
  10. Answer: 108108.
    Working: Vol cone =13π⋅36⋅12=144π= \tfrac{1}{3}\pi\cdot 36\cdot 12 = 144\pi. → Vol ball =43π= \tfrac{4}{3}\pi; n=144π/(4π/3)=108n = 144\pi/(4\pi/3) = 108.
Gyaan Maths · CBSE Class 10 · Chapter 12
Gyaan Maths — CBSE Class 6-10, built for board-toppers.
v1.1 · Feb 2026