Volume and Surface Area Questions

FACTS  AND  FORMULAE  FOR  VOLUME  AND  SURFACE  AREA  QUESTIONS

I. CUBOID

   Let length=l, breadth =b and height =h units. Then,

1. Volume = (l x b x h)

2. Surface area = 2(lb +bh + lh) sq.units

3. Diagonal =$\sqrt{l^2+b^2+h^2}$ units

II. CUBE 

Let each edge of a cube be of length a. Then,

1. Volume = $a^3$ cubic units.

2. Surface area = $6a^2$ sq.units

3. Diagonal = $\sqrt{3}a$ units

III. CYLINDER 

Let radius of base = r and Height (or Length) = h. Then, 

1.Volume = $\left({\mathrm{\pi r}}^2\mathrm{h}\right)$ cubic units 

2. Curved surface area = $\left(2\mathrm{\pi }rh\right)$ sq.units

3. Total surface area = $\left(2\mathrm{\pi rh}+2{\mathrm{\pi r}}^2\right)$ sq.units

IV. CONE 

Let radius of base =r and Height = h. Then, 

1. Slant height, $l=\sqrt{h^2+r^2}$ units

2. Volume = $\left(\frac{1}{3}{\mathrm{\pi r}}^2\mathrm{h}\right)$ cubic units.

3. Curved surface area = $\left(\mathrm{\pi rl}\right)$sq.units 

4. Total surface area = $\left(\mathrm{\pi rl}+{\mathrm{\pi r}}^2\right)$sq.units

V. SPHERE 

Let the radius of the sphere be r. Then, 

1. Volume =$\left(\frac{4}{3}{\mathrm{\pi r}}^3\right)$ cubic units

2. Surface area = $\left(4{\mathrm{\pi r}}^2\right)$ sq.units

VI. HEMISPHERE 

Let the radius of a hemisphere be r. Then, 

1. Volume = $\left(\frac{2}{3}{\mathrm{\pi r}}^3\right)$ cubic units.

2. Curved surface area = $\left(2{\mathrm{\pi r}}^2\right)$ sq.units

3. Total surface area = $\left(3{\mathrm{\pi r}}^2\right)$ sq.units