Question

Question #10244

Answer 1

length of the square face is `4cm`.

Explanation:

Volume of the cuboid is `l*b*h` where, `l, b, h` are the length, breadth and height of the cuboid respectively.

since one of the face of the cuboid is a square, `l=b`
therefore the volume turns out to be, `l*l*h=l^2h=96cm^3`

the area of the rectangular face is given to be, `l*h=24cm^2` (we use `l*h` and not `l*b` as the dimensions of a rectangle cannot be same,)

so plugging in `l*h=24cm^2` into `l^2h=96cm^3` we get,
`l.(24)=96`

`=> l=96/24 cm`

`=> l=4 cm`

and, `h = 24/l`
`h = 24/4 = 6 cm`

so the length of the square face is 4cm. (and the height of the cuboid is 6cm)

verifying,
Volume of a cuboid with dimensions, `4`x`4`x`6`=`96cm^3`
Hence Verified:)

-Sahar.