GCSE - Dimention Questions

can someone help me with dimention questions
i got my higher linear paper coming on this nov
here it is:

The table shows some expressions.
The letters a, b, c and d represent lengths.
π and 2 are numbers that have no dimensions.
Three of the expressions could represent areas.
Tick () the boxes underneath the three expressions which could represent areas.

πabc , π a^3, 2a^2, π a^2 + b, π (a + b), 2(c^2 + d^2 ), 2ad^2
----
2d

'π' means pi and --- means the division line
the answers are the first one, third and the sixth but i dont understand how they are right.
can someone explain the dimention theory

cooldudeman

can someone help me with dimention questions
i got my higher linear paper coming on this nov
here it is:

The table shows some expressions.
The letters a, b, c and d represent lengths.
π and 2 are numbers that have no dimensions.
Three of the expressions could represent areas.
Tick () the boxes underneath the three expressions which could represent areas.

πabc , π a^3, 2a^2, π a^2 + b, π (a + b), 2(c^2 + d^2 ), 2ad^2
----
2d

'π' means pi and --- means the division line
the answers are the first one, third and the sixth but i dont understand how they are right.
can someone explain the dimention theory

First thing to do is remove all the numbers (pi counts as a number).

Each letter a, b, c represents a length.

ab or p^2 = length x length = area

abc or r^3 = length x length x length = volume

Expressions such as ab + c do not exist as that would be an area plus a length and that makes no sense.

However, you can add lengths to lengths or areas to areas or volumes to volumes so these are ok:

ab + cd = area

r^3 - abc = volume

a + d = length

something like (abc)/r = volume / length = area.

This is really hard to explain on here. Hope that helped a bit.

Reply 2

ymca

Basically, any letter e.g. a, b or c stands for a length. Any number such as 1, 2 or pi do not count to forget about any of these. From there it is quite simple:

a + b = length + length = length

ab = length x length = area

abc= length x length x length = volume

Example including numbers

2abc = FORGET ABOUT THE NUMBER. From there it is lxlxl = volume

ab/5 = length x length = area

Hope this helps :smile: