Mensuration is one of the branches of mathematics.This means measurement.It is is being done in our life in many situations.
A Length of cloth we need for stitching,the area of a wall which is being painted, perimeter of the circular garden to be fenced, quantity of water needed to fill the tank. For these kind of activities, we are doing measurements for further needs.
Here, we are going to cover three areas here.
Apart from the examples and practice questions in the above three areas, we also give calculators in this topic which can be used by the students to check their answers which they have found for the questions they have.You can use any of the given calculators to get answer for your questions in seconds.
For example, in his development of integration and calculus, he tried to find a value for π by using circumscribed and inscribed polygons, eventually using 96 sided polygons inside and outside a circle to generate a value for Pi of between 31⁄7 (approximately 3.1429) and 310⁄71 (approximately 3.1408). This range of values is extremely accurate, as the actual value is 3.1416. This is just one example of his inventions.
In this topic we are going study about perimeter, area and volume of different shapes like a cylinder, cone, sphere, hemisphere etc..These shapes are called geometric shapes.
Area of circle = πr2
Circumference of circle = 2πr
Area of semicircle = πr2/2
Circumference of circle = πr
Area of quadrant = πr2/4
Area of equilateral triangle = (√3/4)a2
Perimeter of equilateral triangle = 3a
Area of scalene triangle = √[s(s - a)(s - b)(s - c)]
Perimeter of scalene triangle = a + b + c
Area of right triangle = (b x h)/2
Area of parallelogram = b x h
Perimeter of parallelogram = 2(a + b)
Area of quadrilateral = (1/2) x d x (h1 + h2)
Perimeter of quadrilateral = a + b + c + d
Area of rectangle = l x w
Perimeter of rectangle = 2(l + w)
Area of square = a x a
Perimeter of square = 4a
Area of rhombus = (d1 x d2)/2
Perimeter of rhombus = 4a
Area of trapezoid = h(a + b)/2
Perimeter of trapezoid = a + b + c + d
Length of arc (l) = (θ/360) ⋅ 2πr
When we know the radius "r" of the circle and central angle "θ" of the sector :
Area of the sector = (θ/360°) ⋅ πr2
When we know the radius "r" of the circle and arc length "l":
Area of the sector = (l ⋅ r)/2
Worksheet for length of arc
Curved surface area of cylinder = 2πrh
Total surface area of cylinder = 2πr(h + r)
Volume of cylinder = πr2h
Curved surface area of cone = πrl
Total surface area of cone = 2πr(l + r)
Volume of cone = πr2h/3
Surface area of sphere = 4πr2
Volume of sphere = 4πr3/3
Curved surface area of hemisphere = 2πr2
Total surface area of hemisphere = 3πr2
Volume of hemisphere = 2πr3/3
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