Volume Of Composite Figures Worksheet - Free Printable

Problem: Calculate the volume of composite solids

The task requires solving three problems, ensuring one of them is Question 5. We will calculate the volumes step by step.

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#### Question 1:
The solid is a rectangular prism with a smaller rectangular prism removed from it.

- Dimensions of the larger prism:
Length = 12 in, Width = 8 in, Height = 10 in

- Dimensions of the smaller prism (removed):
Length = 8 in, Width = 3 in, Height = 2 in

Volume of the larger prism:
\[ V_{\text{large}} = \text{Length} \times \text{Width} \times \text{Height} \]
\[ V_{\text{large}} = 12 \times 8 \times 10 = 960 \, \text{in}^3 \]

Volume of the smaller prism:
\[ V_{\text{small}} = \text{Length} \times \text{Width} \times \text{Height} \]
\[ V_{\text{small}} = 8 \times 3 \times 2 = 48 \, \text{in}^3 \]

Volume of the composite solid:
\[ V_{\text{composite}} = V_{\text{large}} - V_{\text{small}} \]
\[ V_{\text{composite}} = 960 - 48 = 912 \, \text{in}^3 \]

Answer for Question 1:
\[ \boxed{912} \]

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#### Question 5:
The solid consists of a cube and a cylinder on top of it.

- Cube dimensions:
Side length = 5 in

- Cylinder dimensions:
Radius = 2 in (since diameter = 4 in), Height = 4 in

Volume of the cube:
\[ V_{\text{cube}} = \text{Side}^3 \]
\[ V_{\text{cube}} = 5^3 = 125 \, \text{in}^3 \]

Volume of the cylinder:
\[ V_{\text{cylinder}} = \pi \times r^2 \times h \]
\[ V_{\text{cylinder}} = 3.14 \times 2^2 \times 4 \]
\[ V_{\text{cylinder}} = 3.14 \times 4 \times 4 = 50.24 \, \text{in}^3 \]

Volume of the composite solid:
\[ V_{\text{composite}} = V_{\text{cube}} + V_{\text{cylinder}} \]
\[ V_{\text{composite}} = 125 + 50.24 = 175.24 \, \text{in}^3 \]

Answer for Question 5:
\[ \boxed{175.24} \]

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#### Question 8:
The solid consists of a rectangular prism and a pyramid on top of it.

- Rectangular prism dimensions:
Length = 23 in, Width = 16 in, Height = 18 in

- Pyramid dimensions:
Base is a square with side length = 16 in, Height = 21 in

Volume of the rectangular prism:
\[ V_{\text{prism}} = \text{Length} \times \text{Width} \times \text{Height} \]
\[ V_{\text{prism}} = 23 \times 16 \times 18 \]
\[ V_{\text{prism}} = 6624 \, \text{in}^3 \]

Volume of the pyramid:
\[ V_{\text{pyramid}} = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]
\[ \text{Base Area} = \text{Side}^2 = 16^2 = 256 \, \text{in}^2 \]
\[ V_{\text{pyramid}} = \frac{1}{3} \times 256 \times 21 \]
\[ V_{\text{pyramid}} = \frac{1}{3} \times 5376 = 1792 \, \text{in}^3 \]

Volume of the composite solid:
\[ V_{\text{composite}} = V_{\text{prism}} + V_{\text{pyramid}} \]
\[ V_{\text{composite}} = 6624 + 1792 = 8416 \, \text{in}^3 \]

Answer for Question 8:
\[ \boxed{8416} \]

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Final Answers:

1. Question 1: \( \boxed{912} \)
2. Question 5: \( \boxed{175.24} \)
3. Question 8: \( \boxed{8416} \)