Overview of Mensuration

Cube (side = a)

• Lateral surface area = 4a²

• Total surface area = 6a²

• Volume = a³

• Curved surface area = 2πrh

• Total surface area = 2πr(r + h)

• Volume = πr²h

• Slant height l =\[\sqrt{h^2+r^2}\]​

• Curved surface area = πrl

• Total surface area = πr(r + l)

• Volume = \[\frac{1}{3}\] × πr²h

• Surface area = 4πr²

• Volume = \[\frac{4}{3}\]πr³

• Curved surface area = 2πr²

• Total surface area of a solid hemisphere = 3πr²

• Volume = \[\frac{2}{3}\]πr³

Let radii r₁ > r₂​, height h, slant height l

• Slant height: l = \[\sqrt{h^2+(r_1-r_2)^2}\]​

• Curved surface area of a frustum: πl(r₁ + r₂)

• Total surface area of a frustum: πl(r₁ + r₂) + πr₁² + πr₂² ​

• Volume: \[\frac{1}{3}\]πh(r₁² + r₂² + r₁ × r₂)

• Lateral surface area = 2h(l + b)

• Total surface area = 2(lb + bh + hl)

• Volume = lbh