Question

The dimensions of Peyton and Parker’s sandbox are t^2m by t^5 m by 3v^2 m. One cubic meter of the sandbox contains 3s^21 grains of sand. How many grains of sand are in the sandbox? A. 27t^10v^2s^21 B. t^10v^2s^21 C. 3t^7v^2s^21 D. 9t^7v^2s^21

Answer 1

Since, the dimensions of sandbox are
`t^2` meter,
`t^5` meter and
`3v^2` meter.

One cubic meter of the sandbox contains
`3s^(21)` grains of sand.

We have to determine the grains of sand are in the sandbox.

So, let us determine the volume of the sandbox.

Since, sandbox is in shape of rectangular prism.

Therefore, Volume of sandbox =
`l * b * h`

=
`t^2 * t^5 * 3v^2`

=
`3t^7 v^2` cubic meters.

Since, one cubic meter of the sandbox contains
`3s^(21)` grains of sand.

Therefore, Number of grains in the sandbox =
`3t^7 v^2 * 3s^(21)`

=
`9v^2 s^(21) t^7`

Option D is the correct answer.