Grade 12 - More exercises.

Area and volume.

1.
Calculate the area of the following 2D figures:
1.1
a rectangle with length = 20 cm and width = 120 mm.
1.2
a right-angled triangle with the right-angled sides equal to 45 cm and 31 cm respectively.
1.3
a triangle with base 30 m and height 5,5 m.
1.4
a parallelogram with length 18 mm and height 8 mm.
1.5
an isosceles triangle with base 38 cm and height 18 cm.
1.6
an equilateral triangle with side = 56 m and height 46,4 m.
1.7
a circle with a radius of 23,4 cm.
1.8
a circle with diameter of 4,65 m.
2.
Calculate the volume and surface area of each of the following regular bodies:
2.1
a rectangular prism wih length 0,85 m, breadth 21 cm and height 185 mm.
2.2
a cube with sides 67 cm long.
2.3
a prism, 34 cm long and having as base a right-angled triangle with right-angled sides 15 cm
and 18 cm long.
2.4
a sphere with radius 3,14 cm.
2.5
a cone with diameter of 45 mm and height = 50 mm.
3.
Calculate the area of every figure in the diagrams and the perimeter of the figures in 3.2, 3.4 and 3.5.
fig. 3.1
fig. 3.2
fig. 3.3
fig. 3.4
fig. 3.5
In 3.3 : H = 14 m ;
d = 20 m
h = 5,5 m
In fig. 3.5 CAB is a right angle
In fig. 3.4 both triangles are
and BC = 13
right angled with ABC
and DAC the right angles
4.
The triangles are right angled triangles
with one side equal to 1. The other side is equal
to the hypotenuse of the preceding triangle.
a is the hypotenuse of the first triangle, b of the
second triangle and c of the third triangle.
4.1
Calculate the value of a, b and c. What do you notice?
4.2
Write down the values of each hyptotenuse of the next 3 triangles.
4.3
Calculate the perimeter of the figure.
4.4
Calculate the area of each triangle and the total area of the figure.
5.
Let fig. 3.3 represent a rondavel with H = 2,8 m, d = 3,5 m and h = 2 m. The roof is a thached roof.
5.1
Calculate the area of the roof.
5.2
Calculate the volume of air in the rondavel.
5.3
Calculate the area of the wall.
6.
The drawing represents a tank. The middle part is a cylinder.
The top and bottom parts are cones.
6.1
Calculate the maximum capacity (volme) of the tank.
6.2
Calculate the area of the metal necessary to construct the tank.
7.
A greenhouse consists of a metal frame in the form of a cylinder with half circles at the ends.
7.1
What area of ground is covered by the greenhouse?
7.2
Can all the ground be used to plant vegetables? Explain.
7.3
Calculate the volume of the air in the greenhouse.
8.
You manufacture tanks in the shape of a rectangle, a cube and a cylinder. Each tank has
a capacity of 5 000 litre. Calculate the dimensions of each tank and the area of the
metal needed to make the tank.
  
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