Surface Areas and Volume

Area

The space occupied by a two-dimensional flat surface. It is measure in square units.

Generally, Area can be of two types

(i) Total Surface Area

(ii) Curved Surface Area

Total surface area

Total surface area refers to area including the base(s) and the curved part.

Curved surface area (lateral surface area)

Refers to area of only the curved part excluding it’s base(s).

Volume

The amount of space, measured in cubic units, that an object or substance occupies. Some shapes are two-dimensional, so it doesn’t have volumes. Example, Volume of Circle cannot be found, though Volume of the sphere can be. It is so because a sphere is a three-dimensional shape.

Below given is the table for calculating Surface area and Volume for the basic geometrical figures:

Name Perimeter Total Surface Area Curved Surface Area Volume Figure
Square 4a a2 —- —-
Rectangle 2(w+h) w.h —- —-
Parallelogram 2(a+b) b.h —- —-
Trapezoid a+b+c+d 1/2(a+b).h —- —-
Circle \(2 \pi r\) \(\pi r^{2}\) —- —-
Ellipse \(2\pi\sqrt{\left ( \frac{a^{2}+b^{2}}{2} \right )}\) \(\pi a.b\) —- —-
Triangle a+b+c \(\frac{1}{2}\times b \times h\) —- —-
Cuboid 4(l+b+h) 2(lb+bh+hl) 2h(l+b) \(l \times b \times h\)
Cube 6a  6a2 4a2 \(a^{3}\)
Cylinder —- \(\pi r(r+h) \) \(2 \pi r h\) \(\pi r^{2} h\)
Cone —- \(\pi r(r+l)\) \(\pi r l\) \(\frac{1}{3}\pi r^{2} h\)
Sphere —- \(4 \pi r^{2}\) \(4 \pi r^{2}\) \(\frac{4}{3}\pi r^{3} \)
Hemisphere —- \(3 \pi r^{2}\) \(2 \pi r^{2}\) \(\frac{2}{3}\pi r^{3} \)

2 Comments

  1. think you give me surface area

    1. You can get all surface area formulas here!
      https://byjus.com/surface-area-formulas/

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