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:

$243=k(3)^2=9k \\ \\ \Rightarrow k= \frac{243}{9} =27 \\ \\ \Rightarrow V=27X^2$

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

$V=27(5)^2=27\times25=\bold{\ 675}$