Here are two pots.
Diagram:
Pot A-
Height: 8cm
Pot B-
Height: 10cm
Pot A and pot B are MATHEMATICALLY SIMILAR.
The area of the base of pot B is 160cm2.
Work out the area of the base f Pot A.
My work:
1)Labelled POt B diagram as having area of abse of 160cm2
2)160*10= 1600cm2
3)Pot A must also equal 160cm2 if both pots are MATHEMATICALLY SIMILAR.
4)So, 160cm2/ 8cm= 20cm
5) The area of ase of pot a is 20cm2 ???
I am not really sure please help!!
areas grow as the square of the linear factor. So the areas are
A:B = (8:10)^2 = 64/100 = 16/25
A/160 = 16/25
A = 16*160/25 = 102.4 cm^2
Steve i had written that same answer in my exam and had gotten it wrong?????
To calculate the area of the base of Pot A, you need to apply the concept of similarity. Since Pot A and Pot B are mathematically similar, their corresponding dimensions are in proportion.
Let's assume that the area of the base of Pot A is "x" cm².
Since the pots are similar, we can set up a proportion between the heights and the areas of their bases:
Height of Pot A / Height of Pot B = Area of base of Pot A / Area of base of Pot B
Given that:
Height of Pot A = 8 cm
Height of Pot B = 10 cm
Area of base of Pot B = 160 cm²
Substituting these values into the proportion:
8 cm / 10 cm = x cm² / 160 cm²
To solve for x, cross-multiply and then divide:
8 cm * 160 cm² = 10 cm * x cm²
1280 cm² = 10x cm²
Dividing both sides by 10:
1280 cm² / 10 = x cm²
128 cm² = x cm²
Therefore, the area of the base of Pot A is 128 cm².
To determine the area of the base of Pot A, we need to use the fact that Pot A and Pot B are mathematically similar.
Mathematical similarity means that the corresponding sides of the two pots are proportional. In this case, since we are interested in the area of the base, we can use the ratio of the heights of the pots to find the ratio of the areas of their bases.
In your work, you correctly multiplied the area of Pot B's base by its height to get 1600 cm². However, there is an error in step 4. Instead of dividing 160 cm² by 8 cm, we should divide 1600 cm² by 10 cm (the height of Pot B).
So the correct calculation is: 1600 cm² / 10 cm = 160 cm².
Therefore, the area of the base of Pot A is 160 cm², not 20 cm² as you mentioned.
To summarize:
1) The area of the base of Pot B is 160 cm² (given).
2) Multiply the area by the height of Pot B: 160 cm² * 10 cm = 1600 cm².
3) Divide the result by the height of Pot A (which is 8 cm) to find the area of the base of Pot A: 1600 cm² / 8 cm = 200 cm².
So, the area of the base of Pot A is 200 cm².