Revision: Mensuration >> Volume and Surface Area of Solids (Cylinder, Cone and Sphere) Maths (English Medium) ICSE Class 10 CISCE

A cylinder is a three-dimensional solid figure that has two identical circular bases joined by a curved surface at a  particular distance from its centre, which is its height.

The solid obtained on revolving a right-angled triangle about one of its sides (other than the hypotenuse) is called a cone or a right circular cone.

A sphere is a solid obtained by revolving a circle about any one of its diameters.
The radius of the sphere is equal to the radius of the circle revolved.

When a solid sphere is cut by a plane passing through its centre into two equal and identical parts, each part is called a hemisphere.

Curved surface area of a cylinder = circumference of base × height

                                                        = 2πrh

Total surface area = Curved surface area + 2 (Area of cross-section)

                               = 2πrh + 2πr²

                               = 2πr(r + h)

Volume = Area of cross-section × height (or, length)

              = πr²h

• Thickness = R−r

• External curved surface = 2πRh

• Internal curved surface = 2πrh

• Total Curved Surface Area  = 2πh(R + r)

• Area of cross-section = π(R² − r²)

• Total Surface Area = 2πh(R + r) + 2π(R² − r²)

• Volume of material = π(R² − r²)h

• Volume = \[\frac{1}{3}\pi r^2h\]

• Curved (lateral) surface area = πrl or \[\pi r\sqrt{h^{2}+r^{2}}\]
  (\[l=\sqrt{h^2+r^2}\])
  

• Total surface area = $\pi r(l+r)$

Sphere (radius = r)

• Volume =\[\frac{4}{3}\pi r^3\]

• Surface Area = 4πr²

Spherical Shell (external radius R, internal radius r)

• Thickness = R − r

• Volume of material = \[\frac{4}{3}\pi(R^3-r^3)\]

Volume of hemisphere \[=\frac{2}{3}\pi r^3\]

Curved surface area (CSA) = 2πr²

Total surface area (TSA) = 3πr²