Formula Sheet – Surface Area & Volumes – Class X

1. Cuboid :

(a) Lateral surface area = 2h(l + b)
(b) Surface area = 2(lb + bh + lh)
(c) Volume = lbh
(d) Length of diagonal =\sqrt{l^2+b^2+h^2}

where l, b, h are length, breadth and thickness of the cuboid.

2. Cube :

(a) Lateral surface area =4l^2
(b) Surface area =6l^2
(c) Volume =l^3
(d) Length of diagonal =\sqrt{3l}

where, l is the edge of the cube.

3. Cylinder :

r = radius, h = height
(a) Area of curved surface  =2\pi rh
(b) Total surface area =2\pi r^2+2\pi rh=2\pi r\ (r+h)
(c) Volume =\pi r^2h
(d) Curved surface area of hollow cylinder =2\pi rh(R+r)
(e) Total surface area of hollow cylinder 2\pi h\ (R+r)+2\pi (R^2-r^2)

4. Cone :

r = radius, h = height, l = slant height.

(a) Curved surface area =\pi rl=\pi r\ \sqrt{h^2+r^2}
(b) Total surface area =\pi r^2+\pi rl=\pi r\ (r+l)
(c) volume =\dfrac{1}{3}\pi r^2h

5. Sphere : r = radius

(a) Surface area =4\pi r^2
(b) volume =\dfrac{4}{3}\pi r^3

6. Hemisphere (solid) : r = radius

(a) Curved surface area =2\pi r^2
(b) Total surface area =3\pi r^2
(c) volume =\dfrac{2}{3}\pi r^3

7. Spherical Shell :

Outer radius = R,
Inner radius = r

(a) Surface area (outer) =4\pi R^2
(b) Surface area (inner) =4\pi r^2
(c) volume of the material =\dfrac{4}{3}\pi (R^3-r^3)=\dfrac{4}{3}(R-r)(R^2+Rr+r^2)

8. When a cone is cut by a plane parallel to the base of the cone, then the portion between the plane and the base is called the frustum of the cone.

(a) Slant height of the frustum, l=\sqrt{h^2+(R-r)^2}
(b) Volume of the frustum of the cone =\dfrac{\pi h}{3}[R^2+r^2+Rr]
(c) Lateral surface area of the frustum of the cone =\pi l(R+r)
(d) Total surface area of the frustum of the cone = (area of the base) + (area of the top) + (lateral surface area)

=[\pi R^2+\pi r^2+\pi l\ (R+r)]\\  =\pi[R^2+r^2+l\ (R+r)].

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