The document Points to Remember- Mensuration Class 8 Notes | EduRev is a part of the Class 8 Course Class 8 Mathematics by Full Circle.

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**Points to Remember**** **

- Area of a parallelogram = Base * Height
- Area of a triangle = 1/2 * Base * Height
- Area of a trapezium = 1/2 * [Sum of parallel sides] * Height
- Area of a rhombus = 1/2 * Product of diagonals
- Surface area of

(i) a cuboid = 2[lb + bh + hl]

(ii) a cube = 6l^{2}

(iii) a cylinder = 2πr(r + h) - Volume of

(i) cuboid = l * b * h

(ii) cube = l^{3}

(iii) cylinder = πr^{2}h - 1 m
^{3}= 1000 litres

**We Know That**

A square, a rectangle, a trapezium, a rhombus, a parallelogram, a triangle, a circle, etc., are plane figures and the surfaces enclosed by their boundaries are called areas. We have formulae to find their areas. The perimeter is the distance around a figure. The plane figures are also called 2-D shapes. The solids such as cubes, cuboids, cylinders are called 3-D shapes. A 3-D shape is bounded by faces. These faces can be rectilinear or curved or both.

We also know that:

(i) The area of a square = Side * Side

(ii) The area of a rectangle = Length * Breadth

(iii) The area of a circle = πr^{2} [where r is the radius]

(iv) The area of triangle = 1/2 * Base * Altitude

(v) The area of a parallelogram = Base * Height

Note:I. All angles of a regular polygon have equal degree measures.

II. All sides of a regular polygon are equal in length.

**Solved Examples:****Q1. What length of a solid cylinder which is 2 cm in diameter must be taken to recast into a hollow cylinder of external diameter 20 cm, 0.25 cm thick and 15 cm long?a. 54.06 cmb. 74.06 cmc. 34.06 cmd. 64.06 cmSolution: **B. The diameter of the solid cylinder = 2 cm or the radius = 1 cm; height h =?

V1 = πr²h = π(1)²h = πh

For the hollow cylinder, H = 15 cm; external diameter = 20 cm or external radius = 10 cm. Hence, internal diameter = 10-0.25 (thickness+ = 9.75 cm. Therefore,

V2 = π [ 10² – (9.75²) ] × 15 = 15π × 19.75 × 0.25

Also, V

h = 74.06 cm

a. 7.96 m

b. or 7.96 cm

c. 7.96 cm²

d. 9.61 cm²

Solution:

A =2πrh

500 = 2 × 3.14 × r × 10

500 = 62.8r

r = 500/62.8

= 7.96

Therefore the radius of the cylinder is 7.96 cm

Solution:

Area of the circle is πr²

= 3.14 × 10²

= 3.14 × 100

=314

Hence the area of the region the horse can graze is 314cm²

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