To calculate the volume of a composite solid consisting of a cube and a square-based pyramid, we need to find the volumes of each component separately and then add them together.
### 1. Volume of the Cube
The formula for the volume of a cube is \( V = a^3 \), where \( a \) is the edge length of the cube.
Given:
- Edge length of the cube \( a = 28 \) cm
\[ V_{\text{cube}} = 28^3 \]
\[ V_{\text{cube}} = 28 \times 28 \times 28 \]
\[ V_{\text{cube}} = 21952 \text{ cm}^3 \]
### 2. Volume of the Square-Based Pyramid
The formula for the volume of a square-based pyramid is \( V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \).
Based on the given information:
- The base edge length of the square-based pyramid will be the same as the edge length of the cube, \( 28 \) cm.
- The height of the pyramid \( h = 16 \) cm.
First, calculate the base area of the pyramid:
\[ \text{Base Area} = \text{side}^2 = 28^2 \]
\[ \text{Base Area} = 28 \times 28 \]
\[ \text{Base Area} = 784 \text{ cm}^2 \]
Now, calculate the volume of the pyramid:
\[ V_{\text{pyramid}} = \frac{1}{3} \times 784 \times 16 \]
\[ V_{\text{pyramid}} = \frac{1}{3} \times 12544 \]
\[ V_{\text{pyramid}} = 4181.33 \text{ cm}^3 \]
### Total Volume of the Composite Solid
To find the total volume of the composite solid, we add the volume of the cube and the volume of the pyramid:
\[ V_{\text{total}} = V_{\text{cube}} + V_{\text{pyramid}} \]
\[ V_{\text{total}} = 21952 + 4181.33 \]
\[ V_{\text{total}} = 26133.33 \text{ cm}^3 \]
So, the volume of the composite solid is \( 26133.33 \text{ cm}^3 \).
Show a composite solid consisting of a cube of edge 28cm and a square-based pyramid of height 16cm. Calculate the volume of the solid
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