Facts that Matter: Surface Areas & Volumes | Mathematics (Maths) Class 10 PDF Download

1. Cube

(i) Volume = (a³) cu. units.
(ii) Lateral surface area = [4a²] sq. units.
(iii) Total surface area = [6a²] sq. units.

2. Cuboid

 For a Cuboid of length = l, breadth = b and height = h, we have:

(i) Volume = (l × b × h) cu. units.
(ii) Lateral surface area = [2 (l + b) × h] sq. units.
(iii) Total surface area = [2 (lb + bh + hl] sq. units.

3. Cylinder

(i) Volume = πr²h cu. units.
(ii) Curved surface area = 2πrh sq. units.
(iii) Total surface area = 2πr (h + r) sq. units.

4. Hollow Cylinder

(i) Volume= [External volume] − [Internal volume]
=(πR²h − πr²h) cu. units = π(R² − r²) cu. units.
(ii) Curved surface area= [External S.A.] + [Internal S.A.]
=[2πRh + 2πrh] sq. units = 2πh (R + r) sq. units
(iii) Total surface area= (curved S.A.) + (area of the base-ring)
= [(2πRh + 2πrh) + 2 (πR² − πr²)] sq. units
= [(2πh (R + r) + 2π (R² − r²)] sq. units

5. Cone

(i) Volume = 1/3 πr²h cu. units.
(ii) Curved surface area = πrl sq. units.
(iii) Total surface area = [Curved surface area] + [Area of base]
= [πrl + πr²] sq. units = πr (l + r) sq. units.

6. Sphere

(i) Volume = 4/3 πr³ cu. units.
(ii) Curved surface area = 4πr² sq. units.
(iii) Total surface area =4πr²sq. units.     

7. Hemisphere

(i) Volume = 2/3 πr³ cu. units.
(ii) Surface area = 2πr² sq. units.
(iii) Total surface area = 3πr² sq. units.