Perimeter
What is perimeter?
The total length of a shape's boundary.
What is area?
The measure of how much space a shape takes up on a surface.
Recall the formula for calculating the circumference of a circle
What is volume?
The measure of how much 3D space an object occupies.
Recall Pythagorean theorem.
c2 = a2 + b2
What is the perimeter of a square with a side length of 15cm?
15x4 = 60cm
What is the area of a square with a side length of 4cm?
A = 4 x 4
= 16cm2
A circle has a diameter of 18cm. Calculate its circumference.
C = 56.55cm
What is the formula for volume?
V = Ah
Which side of the triangle is "c"?
Hypotenuse
A rectangular pool is 7.5m long and 3.5m wide. Calculate its perimeter.
P = 7.5 + 7.5 + 3.5 + 3.5
= 22m
What is the area of a circle with a diameter of 10cm? Answer to two decimal places.
A = pi x 52
= 78.54cm2
A circle has an area of 200cm2. Calculate the radius to three decimal places.
7.979cm
What is the volume of a cube with a side length of 18m?
V = 18 x 18 x 18 = 5832m3
A triangle has a base of 2m and a height of 5m. Calculate the length of the hypotenuse correct to two decimal places.
c2 = a2 + b2
c = sqr (22 + 52)
c = 5.39m
A square has a side length of 9cm. Determine the side length of a equilateral triangle with the same perimeter.
Square perimeter = 9x4 = 36cm.
Equilateral triangle means it has 3 sides of the same length. Therefore, 36/3 = 12cm.
The side length of the triangle is 12cm.
A triangle has a base of 5m and a height of 120cm. Calculate its area to two decimal places.
Area = (5 x 1.2)/2 = 3m2
Or (500 x 120)/2 = 30 000cm2
You have a robot with wheels that are 4cm in diameter. You want your robot to travel 100cm. How many revolutions (full turns) must the wheels make?
Circumference of the wheels are 12.57cm. Therefore, 100cm/12.57cm is 7.96.
The wheel must make 8 revolutions.
A triangular prism has a cross-sectional area of 15m2 and a volume of 3450m3. Calculate its height.
V = Ah
h = V/A
h = 3450m3/15m2
h= 230m
The distance from a point on the ground to the base of a tree is 18m.
The tree is 40m tall.
Calculate the distance from the point on the ground to the top of the tree to two decimal places.
c2 = a2 + b2
c = sqr (182 + 402 )
c = 53.86m
Therefore, the distance from the point on the ground to the top of the tree is 53.86m
A right-angled triangle has a base length of 9cm and a height of 6cm. Calculate its perimeter to two decimal places.
Hypotenuse = c2 = a2 + b2
c2 = 92 + 62
c = 10.82
P = 10.82 + 9 + 6 = 25.82cm
A rectangular room is 7m long and 2m wide. The floor is to be covered with square carpet tiles measuring 5cm by 5cm. How many tiles are needed to cover the floor assuming there are no gaps between the tiles?
Area of the room = 700 x 200 = 140,000cm2
Area of a tile = 5x5 = 25cm2
Number of tiles = 140,000/25 = 5600
Therefore, 5600 tiles are required to cover the floor.
Square area = 100m2
Circle area = 28.27m2
100/28.27 = 3.5
Therefore, you could fit 3 circles.
A cylinder with a radius of 3m and a height of 10m is filled once with water and tipped into a bigger cylinder with a cross-sectional area of 113.1m2. What height would the water be in the larger cylinder? Answer to one decimal place.
Volume of smaller cylinder = Ah = pi x 32 x 10 =282.74m3
Therefore, volume within the larger cylinder will also equal 282.74m3.
Larger cylinder water height:
V = Ah
h = V/A
h = 282.74m3/113.1m2
h = 2.5m
The height of the water in the larger cylinder will be 2.5m
A hiker starts at point A and walks 30km south and then west, ending up 50km directly from his starting point A. How far west did he walk?
c2 = a2 + b2
b2 = c2 - a2
b2 = 502 - 302
b = 40km