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

Answer:

Prism Y

$Height = 12in$

$Length = 6in$

$Width = 4in$

$Volume = 288in^3$

Prism Z

$Height = 18in$

$Length =10in$

$Width = 10in$

$Volume = 1800in^3$

$Total = 2088in^3$

Step-by-step 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:

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

$Total = 2088in^3$