Question

a) The area of a bathroom on a house plan is 5 cm2. Find the area of the bathroom if the map has a scale of 1 : 100.
b) The area of a kitchen is 25 m2.
i) Change 25 m2 to cm2.
ii )Find the area of the kitchen on a plan if the scale of the plan is 1 : 120.
c) The volume of a swimming pool from its construction plan is calculated to be 20 cm3. Find the volume of the pool if the plan has a scale of 1 : 75.
c) The total surface area of the wings on a 747 is 120 m2.
i) Change 120 m2 to cm2.
ii) Find the total surface area of the wings on a scale model built using the scale 1:80.

Answer 1

Its wrong @OrangeMaster . Answer is 500,000. I just don't know how to get there. I need steps for everything.

Answer 2

Are you sure it's not 50,000?

Since the 1:100 is a linear ratio, for area, you need to square it. To explain why, imagine you had a square with a side length of 2 in. The area would be 4 sq. in. If you scaled it up by a factor of 3, then the new side length would be 6 in and the new area would be 36 sq. in. So while the side scaled up by 3, the area scaled up by 9.

Same thing with your problem. if the linear dimensions scaled up by 100, then the area would scale up by 100*100 = 10,000

So if the house plan area was 5 cm^2, the actual area would be 50,000 cm^2

Answer 3

5cm^2=5*1cm*1cm=5*100cm*100cm=50000cm^2

Answer 4

Thats what I got, but thats what the answers say. Anyhow, I am more or less stuck on the other questions. Can you please help me with those? @mtbender74 @shamim

Answer 5

i wouldn't be surprised if the answer was a misprint. it happens more often than you'd think.

what are the others? i can take a look and see if i can help...

Answer 6

Yeah it is a misprint. I need help with C and D. Thanks! @mtbender74

Answer 7

Actually I am fine with D now, just stuck on C

Answer 8

For volume, the scale factor needs to be cubed...since the linear scale factor is 75, the vloume scale factor would be 75*75*75=421,875

Answer 9

the units will give you a clue as to how the scale factor relates...for area we use cm^2, in^2, etc. that tells you that you need to square the scale factor

for volume, we use cm^3, in^3, etc. that tells you that you need to cube the scale factor