SOLIDS

Cube

A six–faced solid figure with all faces equal and adjacent faces mutually perpendicular is a cube.



If “a” be the edge of a cube,
1. The longest diagonal \(= a\sqrt{3}\) The face diagonal \(= a\sqrt{2}\)
2. Volume \(= a^3\)
3. Total surface area \(= 6 a^2\)


CUBOID or RECTANGULAR BOX



If a,b,c are the edges of a box,
1. The longest diagonal \(= \sqrt{(a^2 + b^2 + c^2)}\)
2. Surface area \(= 2 (ab + bc + ac)\)
3. Volume \(= abc\)


RIGHT CIRCULAR CYLINDER

If r is the radius of base and h is the height, then

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1. Volume = \(\pi r^2 h\)
2. Curved surface area \(= 2 \pi rh\)
3. Total surface area \(= 2 \pi r (r + h)\)
4. If a rectangle of length L and breadth B is rotated about its length to form a cylinder, then \(L = 2 \pi R\) and \(B = h\).
5. If a rectangle of length L and breadth B is rotated about its breadth to form a cylinder, then \(B = 2 \pi R\) and \(L = h\)


RIGHT CIRCULAR CONE



R = radius of base
H = Height
L = slant height \(= \sqrt{(H^2 + R^2)}\)

1. Volume \(= \frac{1}{3} \times (\pi R^2H)\)
2. Curved surface Area \(= \pi R L\)
3. Total Surface Area \(= \pi R (R + L)\)


SPHERE



R = Radius

1. Volume \(= \frac{4}{3} \times \pi R^3\)
2. Surface Area \(= 4 \pi R^2\)