Question

Important please help me

What is the volume of the shaded portion of the
composite figure? Express your answer in terms of A.
O 519[pie] units 3
O 681[pie] units 3
O (600[pie] - 81) units
O (600 – 81[pie]) units

Answer 1

The volume of the shaded portion in the composite figure, excluding the cone inside a triangular pyramid, is
`\(600 - 81\pi\)` units³. Thus, the correct answer is (D)
`\( (600 - 81\pi) \)` units³.

To find the volume of the shaded portion, we need to calculate the volume of the triangular pyramid and subtract the volume of the cone.

1. Volume of Triangular Pyramid:

`\[ V_{\text{pyramid}} = (1)/(3) * \text{Base Area} * \text{Height} \]`

The base of the triangular pyramid is a rectangle with dimensions
`15` and 10, so the base area is
`\(15 * 10\)`. The height of the pyramid is
`12`.

`\[ V_{\text{pyramid}} = (1)/(3) * (15 * 10) * 12 \]`

2. Volume of Cone:

`\[ V_{\text{cone}} = (1)/(3) \pi r^2 h \]`

The diameter of the cone is 9, so the radius r is
`\( (9)/(2) \)`. The height \( h \) is 12.

`\[ V_{\text{cone}} = (1)/(3) \pi \left((9)/(2)\right)^2 * 12 \]`

Now, subtract the volume of the cone from the volume of the pyramid to get the volume of the shaded portion:

`\[ \text{Volume of Shaded Portion} = V_{\text{pyramid}} - V_{\text{cone}} \]\[ \text{Volume of Shaded Portion} = \left((1)/(3) * (15 * 10) * 12\right) - \left((1)/(3) \pi \left((9)/(2)\right)^2 * 12\right) \]`

Now, simplify this expression to get the final answer.

`\[ \text{Volume of Shaded Portion} = (600 - 81 \pi) \]`

Therefore, the correct answer is option (D)
`\( (600 - 81 \pi) \)` units³.

Answer 2

the third one is the answer