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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.

User Xiaodi
by
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1 Answer

5 votes

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

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

A student designed this sculpture. Using the dimensions on the sculpture, find the-example-1
User Markus Benko
by
6.6k points