Geometry question

Practice Question Solving
1

A concrete cuboid block which is hollowed out in the centre is 25cm long. It has an internal diagonal of 10√2 cm and an external base width of 14cm. The density of the concrete is 3 grams per cubic centimetre.
What is the mass of the block in grams?

A 300
B 2400
C 7200
D 7500
E 14700

Hi, can someone help me with this? Seems pretty straightforward but I don’t fully understand the question and how to find the height of the outer block as well as the volume of the inner block. The correct answer is C.

2

I think this article refers to what a hollowed out cuboid is.
Still I can’t figure out which side is the hollow side, or where “the center” is…

3

image
image1196×659 86.3 KB

:boom:

1 Like
4

How do you know that the other side of the other cuboid is also 14cm?

5

Let’s assume we have the Pythagoras as 200=sq(a)+sq(b)

There is only one number which can fulfill this result (200) for addition of the squared values and this is 10.

-10 is also an option but not here for the length. :blush:

6

Is that not assuming that the base is a square though? Surely we dont get given enough information to deduce that?

7

Yeah, I can agree that the sides of the inner block must be 10 x 10 to meet the given diagonal length (assuming this Q only asks for a whole number). But doesn’t 25cm long mean the length of the outer block, not the height? I also don’t understand why the outer base should be a square.

8

I can say it in another way, that there is no other positive number in R (real numbers) than 10 which can create a diagonal of 10(sqr)2 in a rectangular shape. That rectangle will be a square.

I also define a cuboid as an extended cube (hence the name), meaning a cube which has been extended from one side, while the oposite side which is a square (the base), is fixed to the surface plane.
I have seen many strange definitions of cuboid on the internet, which I do not agree with.

Regarding whether height or length, it dependes on how you place the 3D shape on the surface/“floor”. If you do that like in my figure, we’ll call it height, while placing it on the surface with its longest dimension from right to left (or left to right) it is called width. If you place the same dimension in direction away from yourself it is called length. So, it depends on mode of standing.