Quant · Geometry

Mensuration

2 sub-topics · 32 lessons · 64 questions · 18 PYQs

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Mensuration 2D13 lessons · 29 questions · 8 PYQs

Mensuration 3D19 lessons · 35 questions · 10 PYQs

Formula sheet

Area of a circular ring
$\text{ring: }\pi(R^2-r^2)=\pi(R+r)(R-r)$
Area of a square from its diagonal
$\text{square: }A=a^2=\frac{d^2}{2}$
Scaling surface area and volume
$\text{scale factor }k:\ S\to k^2S,\ V\to k^3V$
Cone
$\text{cone: }V=\frac{1}{3}\pi r^2h,\ l=\sqrt{r^2+h^2},\ \text{CSA}=\pi rl$
Rectangle: area, perimeter, diagonal
$\text{rectangle: }A=lb,\ P=2(l+b),\ d=\sqrt{l^2+b^2};\quad 2lb=(l+b)^2-d^2$
Painted cube counts
$\text{painted }n^3\text{ cube: }8,\ 12(n-2),\ 6(n-2)^2,\ (n-2)^3$
Cylinder
$\text{cylinder: }V=\pi r^2h,\ \text{CSA}=2\pi rh,\ \text{TSA}=2\pi r(r+h)$
Melting and recasting
$\text{melting: }V_{\text{before}}=V_{\text{after}}$