Question

A container has a surface area of 3,200 cm squared and a capacity of 16 liters. The surface area of a similar container that has a capacity of 0.25 liter is k cm squared, where k is a whole number to be determined. What is the value of k?

Answer 1

`500\text{ cm}^2`

Explanation:

GIVEN: A container has a surface area of
`3200\text{ cm}^2` and a capacity of
`16\text{ litres}`. The surface area of a similar container that has a capacity of
`0.25\text{ litres}` is
`\text{k}\text{ cm}^2`

TO FIND: value of k.

SOLUTION:

Surface area of large container
`=3200\text{ cm}^2`

Capacity of large container
`=16\text{ litres}`

As the other container is similar

let surface area of other similar container
`=\text{k}\text{ cm}^2`

Capacity of small container
`=0.25\text{ litre}`

As volume of a container is directly proportional to its Capacity

Therefore,

`\frac{\text{surface area of large container}}{\text{surface area of small container}}=(16)/(0.25)`

`(3200)/(k)=64`

`k=500\text{ cm}^2`

Hence the value of
`k` is
`500\text{ cm}^2`