mensuration ppt - class project

MENSURATIONMENSURATIONMENSURATIONMENSURATIONMade by-Made by-

Arnav GosainArnav Gosain

VIII-CVIII-C

Tagore Int. School, EOKTagore Int. School, EOK

Contents

• Introduction• Trapezium• Rhombus• Cube• Cuboid• Cylinder• Table• Question Bank

IntroductionArea of• a trapezium =half of the sum of the

length of parallel sides x perpendicular distance between them.

• a rhombus =half the product of its diagonals {d1 x d2}

• Surface area of a solid is the sum of the areas of its faces.

Introduction continued…

Surface area of• a cuboid =2(lb +bh +hl)• a cube =6l² • a cylinder =2πr (r+h)• Volume –amount of region occupied

by a solid is called its volume.

Introduction continued…

• Volume of a cuboid=l x b x h a cube =l³ a cylinder= πr²h• 1 cm³=1ml• 1l=1000 cm²• 1 m³=1000000 cm³=1000 l

TRAPEZIUM• A trapezium is a quadrilateral whose two

sides are parallel.• ABCD is a trapezium such that AB and CD

are its two parallel sides while AD and BC are its non-parallel sides.

• Each of the two parallel sides of b trapezium is called base of the trapezium.

• The distance between the two bases (parallel sides) is called the height or altitude of the trapezium.

• Area of trapezium =half of the sum of the length of parallel sides x perpendicular distance between them.

A

D C

B

Cube• A cube is b 3-D figure whose

length , breadth and height are equal. It has six faces and all are squares and identical.

• Surface area of a cube = 6 x (length of the side)²

• Volume of a cube = (side)³

Rhombus

• It is a quadrilateral whose all sides are equal out of which 2 opposite sides are parallel and none of the angles are right angles.

• Area of rhombus=½ x d1 x d2,where d1 and d2 are 2 diagonals

CUBOID• A cuboid is b 3-D figure which has

six rectangular faces and opposite faces are identical.

• There are three pairs of identical faces.

• Surface area= 2x(lb + bh +lh)• Volume= l x b x h

Cylinder • Cylinder is a 3–D figure which has

one curved surface and two circular faces which are identical.

• Surface area of cylinder= 2πr (r + h)

• Volume of cylinder= πr²h

Table

Figure Volume Surface area

Cuboid L x b x h 2(lb +bh +hl)

Cube 6( l )² l³

Cylinder πr²h 2πr (r + h)

Question Bank Multiple-choice Questions

(i) Area of triangle (a) b x b (c) b x b (b) ½ x b x h (d) b x a Ans- ½ x b x h (ii) If the number of cement bags used to

construct a path is needed, then the formulae to find the number of cement bags is -

(a) area of path + area cemented by 1 bag

(b) Area of the path x area of place cemented by 1 bag

(c) Area of the path / area of the cemented place by 1 bag

(d) none of theseAns- Area of the path / area of the

cemented place by 1 bag (iii) What is the area of circle? (a) b x h (c)πr²

(b) l x b (d) all of theseAns- πr²(iv) Area of the rhombus- (a) [area of triangle-1 + triangle-2] (b) length x breadth (c)½h(a+b) (d) diagonal 1 x diagonal 2Ans- diagonal 1 x diagonal 2(v) Volume

of a cylinder is (a) l x b x h (b)l³ (c)πr²h (d) None of these

Ans- πr²h

(vi) How many centimeters make a litre? (a)100 cm (b)1000 cm³

(c)both (b) and (a) (d) All of the aboveAns- b)1000 cm³ (vii)How many pairs of faces in cuboids are

identical? (a) 3 pairs (b) 6 pairs (c) 5 pairs (d) 10

pairsAns- 3 pairs (vii) Perimeter of parallelogram (a) l x b (b) 2(l + b) (c) 4 x sides (d)

None of theseAns- None of these

(ix) Perimeter of circle (a) 2(l+b) (b) 3s (c) 2πr (d) 4sAns- 2πr (x) Which are identical parts in cylinder (a) One curved surface and three circular

faces (b) Two curved surface and one circular face (c) Both (a) and (b) (d) None of theseAns- None of these Correct answer-One curved surface and two

circular faces

Short answer type questions(1) What is triangulation?Ans- Splitting a quadrilateral into triangles, finding their areas

and hence that of parallelogram(2) Find the area of a rhombus whose diagonals are of

lengths 10 cm and 8.2cm .Ans- Area of rhombus= d1x d2 where d1,d2 are lengths of

diagonals . =10 x 8.2 cm² =41 cm²(3) Find the volume of the cube which has dimensions 2 x 2

x2 cmAns- Volume of the cube = 6(l)² = 6(2)²=6 x 4 = 24 cm³ (4) In which unit is the volume expressed?Ans- cubic centimeter (cm³)

(5)Find the area of quadrilateral PQRS shown in the figure.

Ans- d=5.5 cm,h1=2.5 cm,h2=1.5 cm Area=½ d(h1 + h2) =½ x 5.5 x

(2.5+1.5)cm² =½ x 5.5 x 4 cm² =11 cm²P

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