ChandlerBong wrote:
The length, breadth, and height of a cuboid are integers and greater than one. If the area of one face of the cuboid is 24cm^2, what is the volume of the cuboid?
(1) The product of the area of the two faces of the cuboid is 96cm^2
(2) Area of one of the faces of the cuboid is 8cm^2
Given that the area of one side of the cube is \(24 \text{cm}^2\)
Possible dimensions of the side = (2,12), (12,2), (3,8), (8,3), (4,6), and (6,4)
Statement 1(1) The product of the area of the two faces of the cuboid is 96cm^2As the area of one of the sides is \(24 \text{cm}^2\), the area of the second side is \(4 \text{cm}^2\). We can have only one combination of the values of the side, i.e. when the sides are 2 cms each.
Note, that one of the sides must be common to the side with area \(24 \text{cm}^2\), and the side should measure 2 cm.
Hence, the dimensions of the cube are 12 cm * 2 cm * 2 cm.
Volume =\( 48 \text{cm}^3\)
The statement is sufficient and we can eliminate B, C, and E.
Statement 2(2) Area of one of the faces of the cuboid is 8cm^2The possible dimensions of the side are (4,2) and (2,4)
Let's assume that the side with measure 4 is the common side. In that case, the dimensions of the cube are 6cm * 4 cm * 2 cm. Volume = \( 48 \text{cm}^3\)
Let's assume that the side with measure 2 is the common side. In that case, the dimensions of the cube are 12cm * 2 cm * 4 cm. Volume = \( 96 \text{cm}^3\)
Hence this statement is not sufficient.
Option A