unit 2.5 , 2.6 - mensuration , coordinate geometry

Question 1

perimeters

Answer 1

1) square = 4 x length
2) rectangle = 2(length + breadth)
3) circle (circumference) = 2πr / πd

4) arc length
- θ/360° x 2πr (degrees)
- rθ (rad)

Question 2

areas

Answer 2

1) square = length²
2) rectangle = length x breadth

3) triangle
- 1/2 x breadth x height
- 1/2 ab sin C

4) //gram = breadth x height
5) trapezium = 1/2 (a + b) x height
6) rhombus = breadth x height
7) circle = πr²

8) sector
- θ/360° x πr² (degrees)
- 1/2 r² θ (radians)

9) segment = 1/2 r² (θ - sin θ) [radians]

Question 3

volumes

Answer 3

1) cuboid = length x breadth x height
2) cylinder = πr²h
3) prism = x-sectional area x length
4) pyramid = 1/3 x base area x height
5) cone = 1/3 π r² h
6) sphere = 4/3 π r³
7) hemisphere = 2/3 π r³

Question 4

curved surface areas

Answer 4

1) cylinder = 2π r h
2) cone = πr x slant height
3) sphere = 4π r²
4) hemisphere = 2π r²

Question 5

total surface areas

Answer 5

1) cuboid = 2(Lb + Lh + bh)
- > L = length , b = breadth , h = height

2) cylinder = 2π rh + 2π r²
3) prism = perimeter of base x height + 2(base area)
4) cone = πrl + πr²
5) sphere = 4π r²
6) hemisphere = 2π r² + πr² OR 3π r²

Question 6

formulas for coords geom

Answer 6

1) gradient (m) = y2 - y1 / x2 - x1
2) distance = root (x2 - x1)² + (y2 - y1)²
3) eqn of line: y = mx + c

4) types of gradients
- vertical line ; m is undefined
- horizontal line ; m = 0
- line cuts thru centre , O ; c = 0
• c -> point whr line cuts thru the y-axis