CBSE Class 10 Maths: Surface Areas & Volumes — Notes 2026

Cube and Cuboid

• Cuboid: SA = 2(lb + bh + lh); V = lbh; diagonal = √(l²+b²+h²)
• Cube: SA = 6a²; V = a³; diagonal = a√3
• CBSE: paint/wallpaper (SA), packing/filling (volume) word problems

Cylinder

• CSA = 2πrh; TSA = 2πr(r+h); V = πr²h
• Hollow cylinder: volume = π(R²−r²)h; used in pipes, straw problems
• CBSE: water tank capacity, metal rod to cylinder, cylinder made from rectangular sheet

Cone

• Slant height l = √(h²+r²); CSA = πrl; TSA = πr(l+r); V = ⅓πr²h
• CBSE: canvas required for conical tent (CSA); volume of material in solid cone
• Cone inverted and filled with water — find volume of water

Sphere and Hemisphere

• Sphere: SA = 4πr²; V = (4/3)πr³
• Hemisphere: CSA = 2πr²; TSA = 3πr²; V = (2/3)πr³
• Hollow sphere: V = (4/3)π(R³−r³); used in ball bearings, hollow metal spheres

Frustum of Cone

• CSA = π(R+r)l; l = √[h²+(R−r)²]; TSA = πl(R+r)+π(R²+r²)
• V = (πh/3)(R²+r²+Rr)
• CBSE: bucket (frustum) capacity; wax candle frustum; earthen pots

Conversion of Solids

• Melting/recasting: volumes equal; change in dimensions calculated
• n small spheres from one large sphere: R³ = nr³; find r or n
• CBSE: metallic sphere melted to form wire of radius r and length l; cone melted to sphere

CBSE Exam Numericals

• A toy is in form of hemisphere of radius 3.5 cm surmounted by cone of same radius; height of cone = 4 cm. Find TSA
• Frustum with R=12 cm, r=3 cm, h=10 cm; find volume and CSA
• Water flowing through cylindrical pipe at 2 m/s fills tank in 30 min; find volume of tank