Answer:
[tex]500\text{ cm}^2[/tex]
Step-by-step explanation:
GIVEN: A container has a surface area of [tex]3200\text{ cm}^2[/tex] and a capacity of [tex]16\text{ litres}[/tex]. The surface area of a similar container that has a capacity of [tex]0.25\text{ litres}[/tex] is [tex]\text{k}\text{ cm}^2[/tex]
TO FIND: value of k.
SOLUTION:
Surface area of large container [tex]=3200\text{ cm}^2[/tex]
Capacity of large container [tex]=16\text{ litres}[/tex]
As the other container is similar
let surface area of other similar container [tex]=\text{k}\text{ cm}^2[/tex]
Capacity of small container [tex]=0.25\text{ litre}[/tex]
As volume of a container is directly proportional to its Capacity
Therefore,
[tex]\frac{\text{surface area of large container}}{\text{surface area of small container}}=\frac{16}{0.25}[/tex]
[tex]\frac{3200}{k}=64[/tex]
[tex]k=500\text{ cm}^2[/tex]
Hence the value of [tex]k[/tex] is [tex]500\text{ cm}^2[/tex]
