Question

A student designed this sculpture. Using the dimensions on the sculpture, find the dimensions of each rectangular prism. Then calculate the volume of each prism.

Answer 1

Prism Y

`Height = 12in`

`Length = 6in`

`Width = 4in`

`Volume = 288in^3`

Prism Z

`Height = 18in`

`Length =10in`

`Width = 10in`

`Volume = 1800in^3`

`Total = 2088in^3`

Explanation:

Given

See attachment for sculpture

Solving (a) The dimension and volume of Y

From the attachment

`Height = 18 - 6`

18 in is the height of Z and 6in represents the length (height) of the unoccupied space by Y

So:

`Height = 12in`

`Length = 16 - 10`

16 in is the total length of the sculpture and 10 in represents the length of Z

So:

`Length = 6in`

`Width = 10 - 6`

10 in is the width of Z and 6in represents the length (width) of the unoccupied space by Y

So:

`Width = 4in`

Hence, the dimension of Y is:

`Height = 12in`

`Length = 6in`

`Width = 4in`

Volume is then calculated as:

`Volume = Length * Width * Height`

`Volume = 12in * 6in * 4in`

`Volume = 288in^3`

Solving (b) The dimension and volume of Z

As identified in (a), the dimensions of Z are:

`Height = 18in`

`Length =10in`

`Width = 10in`

Volume is then calculated as:

`Volume = Length * Width * Height`

`Volume = 18in * 10in * 10in`

`Volume = 1800in^3`

Solving (c): Total volume of the sculpture.

To do this, we simply add up the volumes of Y and Z.

So, we have:

`Total = 288in^3 + 1800in^3`

`Total = 2088in^3`