CAT 2025 Lesson : Mensuration - Concepts & Cheatsheet

1) Basic Formula

Shape	CSA/LSA (Curved surface area/Lateral surface area)	TSA (Total surface area)	Volume
Cuboid	$2(l + b)h$	$2(lb + bh + hl)$	$lbh$
Cube	$4a^2$	$6a^2$	$a^3$
Right Circular Cylinder	$2 \pi r h$	$2 \pi r (h + r)$	$\pi r^2 h$
Right Prism	Perimeter of the base $\times$ $h$	LSA + 2 $\times$ Area of the base	Area of the base $\times$ $h$
Right Circular Cone	$\pi r l$	$\pi r (l + r)$	$\dfrac{1}{3}\pi r^2 h$
Pyramid	$\dfrac{1}{2}\times$ perimeter of the base $\times$ $l$	LSA + Area of Base	$\dfrac{1}{3} \times$ Area of Base $\times$ $h$
Frustum	$\pi (r + R)l$	$\pi (rl + Rl + r^2 +R^2)$	$\dfrac{1}{3} \times \pi h(r^2 + rR + R^2$
Sphere	$4 \pi r^2$	$4 \pi r^2$	$\dfrac{4}{3} \pi r^3$
Hemisphere	$2 \pi r^2$	$3 \pi r^2$	$\dfrac{2}{3} \pi r^3$
Torus	$4 \pi^2 Rr$	$4 \pi^2 Rr$	$2 \pi^2 Rr^2$

2) Other Formulae

(i) Longest Diagonal of a Cuboid =

\sqrt{l^2+b^2+h^2}

(ii) Longest Diagonal of a Cube =

\sqrt{3a}

(iii) In a Right Circular Cone, slant height

l = \sqrt{r^2 + h^2}

(iv) In the Frustum of a Cone, slant height

l = \sqrt{(R - r)^2 + h^2}

(v) In a Torus, r is the minor radius of the circle that is revolved and R is the major radius, i.e. the distance between the centre of the torus and the centre of the circle revolved.

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