CBSE · Class 10 · Mathematics · Chapter 12

Surface Areas and Volumes — Formula Sheet

Board Formulas

9 formulas

1.Cuboid★
$V = l bh, TSA = 2 (l b + bh + h l)$
$l$ : Length · $b$ : Breadth · $h$ : Height
Volume = length × breadth × height. TSA sums the 6 rectangular faces.
2.Cube
$V = a^{3}, TSA = 6 a^{2}$
Special cuboid with all sides equal. Six square faces of side a.
3.Cylinder★
$V = π r^{2} h, CSA = 2 π r h, TSA = 2 π r (r + h)$
CSA = curved surface only. TSA adds the two circular ends.
4.Cone
$V = \frac{1}{3} π r^{2} h, CSA = π r l, TSA = π r (r + l)$
l = slant height = √(r² + h²). CSA is a sector when unrolled.
5.Sphere★
$V = \frac{4}{3} π r^{3}, Surface Area = 4 π r^{2}$
One number to know per formula. Sphere has no edges or vertices.
6.Hemisphere
$V = \frac{2}{3} π r^{3}, CSA = 2 π r^{2}, TSA = 3 π r^{2}$
Half a sphere. TSA = curved half sphere + flat circular base.
7.Slant Height of a Cone
$l = r^{2} + h^{2}$
Direct Pythagoras. Use before applying CSA = πrl.
8.Frustum of a Cone
$V = \frac{1}{3} π h (R^{2} + R r + r^{2}), CSA = π (R + r) l$
A cone with the top sliced off. R, r are the two radii; h is height; l = √(h² + (R−r)²).
9.Volume Conservation on Recasting★
$V_{old} = V_{new}$
When metal is melted and recast, volume stays the same; surface area changes.