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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