Question

The dimensions of a cuboid are in ratio 3:2:1 find the dimensions of the cuboid if it's volume is 48 cubic cm​

Answer 1

Answer:

We know that the dimensions of the cuboid – or rectangular prism – are in the ratio 3:2:1, meaning they can be represented as  3k:2k:1k . Since the surface area of a cuboid is  SA=2(LW+LH+WH) , we can replace the three dimensions with our three unknown dimensional terms:

SA=2(3k⋅2k+3k⋅1k+2k⋅1k)=22k2  

5632 cm2=22k2⟹k=16 cm  

Now that we know  k , we could substitute it back in to determine the length of each side and then multiply them, or just stick with the variable form:

V=LWH=3k⋅2k⋅1k=6k3=24576 cm3

Step-by-step explanation:

hope it helps:)

Answer 2

Answer:

Here are the ratios of the three different sizes of sides:

6:3:2

As you can see, there are 22 portions, as there’s two of each size of side. Divide the total surface area by it. You get 256.

256 is the size of a 1 by 1 unit square. Take its square root to get the length of one unit, which is 16 cm.

Multiply by the ratio to get 16*32*48. Plug those numbers into a calculator to get 24,576.