PLANE and SOLID MENSURATION

Definition Of Mensuration.

Topic dealing with the use of formulae to calculate Perimeters, Areas and Volumes of plain shapes and solid figures.

Surface Area and Volume of SolidsSolid: Geometric figure in three dimensionsSurface Area: Total area of all the surfaces of a solid shape or prismVolume: This is the space occupied by a solid shape or prism

Cube and CuboidCube

LLLTotal Surface Area = 6 x LRemember : Area of one face = L

Volume = L3

Example 1The sides of a cube are 5cm long. Find,Its total surface area,Its volume.5cm5cm5cm

Answers:1.(a). T.S.A = 6 x L = 6 x 5 = 150cm (b) V = L = 5x5x5 = 125cm

Task 1The faces of a cube are 10cm long. Find,Its total surface area,Its volume.

Answers:T.S.A. = 6 X 10 = 600cmV = 10x10x10 = 1000cm

Cube and CuboidCuboidhblTotal Surface Area = 2( l b + b h + l h )Remember: Area of first pair = lb x 2 = 2 l b Area of second pair = b h x 2 = 2 b h Area of third pair = l h x 2 = 2 l hVolume =l x b x h, i.e. V = l b h

Example 2A box has length 15cm, breadth 7cm and height 8cm. Find,Its total surface area,Its volume.

Answers:2. (a) T.S.A.=2 [ (15 X 7) + (7 X 8) + (15 X 8) ] =2 (105 + 56 + 120 ) =2 X 281 =562cm2 (b) V = 15 x7x8 = 105 x 8 = 840cm3

Task 2A cuboid is 4cm long, 2cm broad and 3cm high. Calculate,Its total surface area,Its volume.

Answers:T.S.A. =2 [ (4X2) + (2X3) + (4X3) ] = 2( 8+6+12 ) = 2 X 26 = 46cm2(b) V = 4X2X3 = 24cm3

Triangular PrismREMEMBER: A prism is an object with the same cross section length (L).VOLUME: Area of cross-section x length (L) i.e, V = A X L, where A = (bh). HINT:L in some cases is considered as h = height.T. S. A (Total Surface Area) = Area of the 2 triangles + Area of the 2 equal rectangles + Area of the third rectangle (down).

Example 3A prism has a base in form of an isosceles triangle with the two equal sides of 5cm each and the third side of 8cm long; the height of the prism is 12cm. Calculate, (a) the volume of the prism,(b) the total surface area of the prism. X8cm5cm5cm12cm4cm4cm

Answers:3. (a) V = Area of base x heightHint: First find X = height of base triangle (isosceles) i e, By Pythagoras Theorem,5 = 4 + xx = 5 - 4By completing the square,x = 5 - 4x = 25 16x = 9x =3cmBase area = x 8 x3 =12cmTherefore, Volume = Base Area x height = 12 x 12 = 144cm

. (b) T. S. A. = Area of the 2 triangles + Area of the 2 equal rectangles + Area of the third rectangle Solving 1: A = 2 ( x 8 x 3) = 2 x 12 = 24cm Solving 2: A =2 (12 x 5) = 2 x 60 = 120cm Solving 3: A = 12 x 8 = 96cm Therefore, T. S. A. = 24 + 120 + 96 = 240cm

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