PYTHAGORAS-1

Find the length  AC. [Diagram not to scale]

Suluhu

We will use the PYTHAGORAS theorem [ a² + b² = c² ]

a² + b² = c²

AB² + BC² = AC²

3² + 4² = AC²

9 + 16 = AC²

25 = AC² [Here, we find the square root of 25]

5 = AC

Hence AC = 5mm

CIRCLE PERIMETER-2

Find the perimeter of the circle below

Solution

Diameter = 2xr =2x70=140

So, D=140mm

Perimeter = ∏ x D

                = 22 x 140⁷⁰

                    7₁

                = 22 x 70

                = 1540

Hence perimeter is 1540 mm. 

GEOMETRY-1

Find the value of x in the following figure

Solution

2x + 2x + 8x + 8x = 360⁰

4x + 16x = 360⁰

20x = 360⁰

20x   = 360⁰

20         20

X = 18⁰

Hence x is 18⁰

ALGEBRA-3

AREA OF RECTANGLE-1

Find area of the following rectangle (diagram not to scale)

Solution

Area = Length x width

         = 38 x 20

         =760m²

Hence area is 760m²

LCM-2

Find LCM between 40 and 80

solution

Hence LCM is 80

AREA OF CIRCULAR PRISM-1

Find area of the following circular prism which is closed on both sides

Solution

Area = 2∏rh + 2∏ x r²

=(2 x 22 x 35⁵ x 100) + (2 x 22 x 35⁵ x 35)

           7₁                                7₁

=(2 x 22 x 5 x 100) + (2 x 22 x 5 x 35)

                                           

=(44 x 500) + (44 x 5 x 35)

=22000+ 7700

=29700

Hence area is 29700 cm²