"Question 5 An ant is moving around a few food pieces of different shapes scattered on the floor. For which food − piece would the ant have to take a longer round? Remember, circumference of a circle can be obtained by using the expression c = 2πr, where r is the radius of the circle.
Class 8 Mensuration Page 171"
Answers
Mensuration:
Mensuration is the branch of mathematics which concerns itself with the measurement of Lengths, areas & volume of different geometrical shapes or figures.
Plane Figure: A figure which lies in a plane is called a plane figure.
For e.g: a rectangle, square, a rhombus, a parallelogram, a trapezium.
Perimeter:
The perimeter of a closed plane figure is the total length of its boundary.
In case of a triangle or a polygon the perimeter is the sum of the length of its sides.
Unit of perimeter is a centimetre (cm), metre(m) kilometre(km) e.t.c
Area: The area of the plane figure is the measure of the surface enclose by its boundary.
The area of a triangle are a polygon is the measure of the surface enclosed by its sides.
A square centimetre (cm²) is generally taken at the standard unit of an area. We use square metre (m²) also for the units of area.
Circumference of a circle is the perimeter of a circle.
In a circle the radius is half of the diameter.
The approximate value of π( Pi) is= 22/7
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Solution:
i)
Given:
Diameter = 2.8 cm
Radius= 2.8/2= 1.4 cm
Perimeter of the figure = Perimeter of Semicircular part + Diameter of the part
= πr + 2r
=(22/7) × (1.4) + 2.8
= 22× .2 + 2.8 = 4.4+ 2.8
=7.2 cm
ii)
Given :
Diameter = 2.8 cm
Radius= 2.8/2= 1.4 cm
Perimeter of the figure = Perimeter of Semi-circular part + 2Length + Breadth
= πr +L+ 2B
= 22/7× 1.4 + 2.8+ 2× 1.5
= 22×.2 + 2.8+ 3
=4.4 + 2.8+ 3
=10.2 cm
iii)
Given :
Diameter = 2.8 cm
Radius= 2.8/2= 1.4 cm
Slant height= 2 cm
Perimeter of the shape = Perimeter of Semi-circular part + 2(slant height)
= πr + 2 (slant height)
= 22/7× 1.4 +2+2
=4.4 + 4
=8.4 cm
Hence, the food shape in (b) requires the ant to
cover the more distance.
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