Question

The value V of a square glass varies directly as the square of its length X cm. If the value of a square glass with length 3 cm is $243, find the value of a glass with length 5 cm

Answer 1

Given that the value V of a square glass varies directly as the square of its length X cm.

Then, the variation equation is given by


`V\propto X^2 \\ \\ \Rightarrow V=kX^2`

Given that value of a square glass with length 3 cm is $243, we have:


`243=k(3)^2=9k \\ \\ \Rightarrow k= (243)/(9) =27 \\ \\ \Rightarrow V=27X^2`

Thus, the value of a glass with length 5 cm is


`V=27(5)^2=27*25=\bold{\$675}`