Question

Milton got a paperweight like the one shown below. He needs to fill it with sand to give it weight.

If a = 2 inches, what is the volume of the paperweight?

A.24 in3
B.56 in3
C.16 in3
D.32 in3

Answer 1

Given that, Milton got a paperweight like the one shown in the figure.

The Paper Weight is in the shape of a cuboid and a cube.

Length and breadth of cuboid is a and height of the cuboid is 2a, whereas side of cube is a.

The volume of sand required to fill in the Paper Weight , is equal to the volume of the Paper weight,

Volume of Paper Weight = Volume of cube + Volume of cuboid

We know that, Volume of cube =
`(side)^(3)`

and , Volume of Cuboid =
`length * breadth * height`

Volume of Paper Weight =
`a^(3)+ (a* a *2a)= a^(3) +2a^(3) = 3a^(3)`

Given that , a = 2 inches , then Volume of Paper Weight =
`3 * (2)^(3)= 3* 8 = 24`

`24 \: in^(3)` is the volume of the paperweight.

Option A is the correct solution.

Answer 2

2x2x2 = 8

4 x 2 x 2 = 16

16+8 = 24

Answer is A