Question

Find the volume of the rectangular prism. Express your answer as a simplified mixed number.

Answer 1

The volume of the rectangular prism is
`$43(3)/(16)$` cubic meters.

The volume of a rectangular prism is the product of the length, width and height of the prism. From the image, we can find that the lengths of the sides are
`$8(1)/(4)$` m, 6 m and
`$8(3)/(8)$` m.

To find the volume, we just multiply these side lengths together.

`$\begin{aligned} &\phantom{=}(8(1)/(4)\text{ m}) * (6\text{ m}) * (8(3)/(8)\text{ m}) \\\\ &= \left((33)/(4)\text{ m}\right) * (6\text{ m}) * \left((67)/(8)\text{ m}\right) \\\\ &=(33* 6* 67)/(4* 8) \\\\ &=(1386)/(32) \\\\ &= 43(6)/(32) \\\\ &= 43(3)/(16)\text{ m}^3 \end{aligned}$`

Therefore, the volume of the rectangular prism is
`$43(3)/(16)$` cubic meters.

Answer 2

414 9/16 m³

`414(9)/(16)m^(3)`

Explanation:

The volume of a Rectangular prism is calculated as Length × Width × Height

From the attached diagram,we can see that

The length = 8 3/8 m

The width = 6 m

The height =8 1/4 m

Converting the mixed fraction to improper fraction in other to simplify it better

The length = 67/8 m

The height = 33/4 m

The volume of the rectangular prism =

67/8 m × 6m × 33/4m

= (13266/32)m³

= 6633/16 m³

= 414 9/16 m³

=
`414(9)/(16)m^(3)`