Proportional Shapes
Two rectangles are proportional. The sides of one rectangle are: 2cm and 4cm. The sides of the 2nd rectangle are 6cm and x. What is the value of x?
x = 12cm
2/6 is proportional to 4/12.
What is the square root of 100?
10.
102 = 100
A rättvinkel triangle has measurements of
A= 3cm
B= 4cm
C= x.
What is the value of x? Solve using pythagorean theorem
5cm.
A cube has side measurements of 3cm. What is the volume of the cube?
27 cm3
3 x 3 x 3
(Length x Width x Height)
A picture of a car has a scale of 1:10. The length of the car in the picture is 15cm. What is the length of the car in real life?
150 cm.
1:10 = 15:150
(15 x 10 = 150)
Rectangle A has measurements of 5cm and 10cm.
Rectangle B has measurements of 10cm and 15cm.
Are these rectangles proportional? Yes or No.
No. 5/10 is not proportional to 10/15.
Solve 72.
49.
A rättvinkel triangle has the following measurements:
A = 8cm
B = x cm
C = 10cm
What is the value for B? Solve using pythagorean theorem.
B = 6 cm.
A square-based pyramid has side measurements of 3cm and a height of 4cm. What is the volume of the pyramid?
12cm3
(3 x 3 x 4) / 3
(Length x Width x Height / 3)
A picture of an ant has a scale of 5:1. The length of the ant in the picture is 10cm. What is the length of the ant in real life?
2cm.
5:1 = 10:2.
(10 / 5 = 2)
Two triangles are proportional. Triangle A has measurements of 3cm, 4cm and 10cm. Triangle B has measurements of 12cm, x and y. What are the values of x and y?
x = 16cm and y= 40cm.
3/12 is proportional to 4/16 and 10/40.
Solve 32 x 22
36.
(Power law: Simplify 32 x 22 into 63)
What do you call the long side of the a right angle triangle; the side that is always labeled C?
(Hint: It starts with an H)
The hypotenuse.
A cylinder has a base radius of 2cm and a height of 10cm. What is the volume of the cylinder?
125,6cm3
22 x 3,14 x 10
(r2 x Pi x Height)
If the length scale between two shapes is 1:2, what is the area scale?
1:4
Area Scale = Length Scale2
Triangle A has measurements of 4cm and 15cm.
Triangle B has measurements of 6cm and 20cm.
Are the triangles proportional? Yes or No.
No. 4/6 is not proportional to 15/20.
What do we call a square root that does not give a whole number as its answer? (For example, the square root of 2).
An imperfect square.
(BONUS: Imperfect squares will give you irrational numbers as answers)
A triangle has the following measurements:
A = 7 cm
B = 12cm
C= 15cm.
Is the triangle a rättvinkel triangle? Check by using pythagorean theorem.
No.
72 + 122 does not equal 152
(a2 + b2 = c2)
A triangular prism is a shape that has a triangle at the bottom. The base of the triangle at the bottom is 4cm, the height of the triangle at the bottom if 3cm. The height of the whole prism is 5cm. What is the volume of the prism?
30cm3.
(4 x 3 / 2) x 5
(base x height / 2) x height of prism
If the length scale of two shapes is 1:3, what is the volume scale?
1:27
Volume Scale = Length Scale3
Two rectangles are proportional.
Rectangle A has measurements of 5cm and 9cm.
Rectangle B has measurements of 6cm and x.
What is the measurement for x?
x = 10,8cm.
(To solve:, figure out what you multiply 5 with to turn it into 6. Then multiply 9 by that number to get the value for x.)
Solve (22)3
64.
(Power law: Multiply the exponents first, and then do 26).
A rättvinkel triangle has the following measurements:
A = 11cm
B = 4cm
C = x cm
What is the value for C? Solve using pythagorean theorem, and round your answer to the nearest tenth.
C = 11,7cm.
A sphere has a radius of 2cm. What is the volume of the sphere? Round your answer to the nearest tenth.
33.5cm3
(23 x 3,14 x 4) / 3
(r3 x Pi x 4) / 3
If the scale on a map is 1:1000000, and the distance between two cities on a map is 5cm, what is the distance between the cities in real life? Answer in KM.
50km.
100000cm = 1 km.