# Mensuration

Conversion
$1\text{ m}= 100\text{ cm}$
$1\text{ m}^2= 10,000\text{ cm}^2$
$1\text{ m}^3= 1,000,000\text{ cm}^3$
Parallelogram
Area = $b\times h$
Trapezium
Area = $\dfrac{a+b}{2} \times h$
Circle
Circumference = $2\pi r$
Area = $\pi r^2$
Cuboid
Surface area = $2 (lb + lh + bh)$
Volume = $l \times b \times h$
Cylinder
Surface area = 2 $\times$ base area + curved surface area
= $2 \pi r^2 + 2 \pi r h$
Volume = base area $\times$ height
= $\pi r^2 h$
Prism
Volume = cross-sectional area $\times$ $l$
Pyramid
Volume = $\frac{1}{3} \times$ base area $\times$ height
Cone
Volume = $\frac{1}{3} \times$ base area $\times$ height
= $\frac{1}{3} \pi r^2 h$
Surface Area = base area + curved surface area
= $\pi r^2 + \pi r l$
Sphere
Volume = $\frac{4}{3} \pi r^3$
Surface area = $4 \pi r^2$
Radian & Degree
$180^\circ= \pi \text{ rad}$
Arc length & sector area
Degree
$s = \frac{\theta}{360^\circ} \times 2 \pi r$, where $\theta$ is in degrees
$A = \frac{\theta}{360^\circ} \times \pi r^2$, where $\theta$ is in degrees

Radian
$s = r \theta$, where $\theta$ is in radians
$A = \frac{1}{2} r^2 \theta$, where $\theta$ is in radians

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