Question

20 Mathematically similar wooden blocks are made in a workshop.

There are small blocks and there are large blocks.
The volume of each small block is 300 cm
Given that
the surface area of each small block: the surface area of each large block - 25:36
DO NOT WRITE IN THIS AREA
work out the volume of each large block.

Answer 1

Answer:
`518.4\ cm^3`

Explanation:

Given

The volume of the small block is
`300\ cm^3`

The ratio of the surface area of small to large block is
`25:36`

Suppose the length of the small and large box is a and b

`\therefore \left((6a^2)/(6b^2)\right)=(25)/(36)\\\\\Rightarrow \left((a)/(b)\right)^2=(25)/(36)\\\\\Rightarrow \left((a)/(b)\right)=(5)/(6)\\\\\therefore \text{Ratio of the volumes of two is }\\\\\Rightarrow (a^3)/(b^3)=(5^3)/(6^3)\\\\\Rightarrow (V_s)/(V_l)=(125)/(216)\\\\\Rightarrow V_l=300* (216)/(125)\\\\\Rightarrow V_l=518.4\ cm^3`