To find the volume of the entire object composed of a hemisphere and a cone, we can first calculate the volume of the hemisphere and then add it to the volume of the cone.
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Volume of the cone: Given as 12 m³.
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Height of the cone (h) is equal to the diameter of the hemisphere (D), which means \( h = 2r \), where \( r \) is the radius of the hemisphere.
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Volume of the hemisphere: The formula for the volume of a hemisphere is given by:
\[ V = \frac{2}{3} \pi r^3 \]
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To find the radius \( r \) of the hemisphere, we also need to relate it to the volume of the cone: The volume of a cone is given by:
\[ V = \frac{1}{3} \pi r^2 h \]
Since \( h = 2r \), we can substitute \( h \) into the cone volume formula:
\[ V_{\text{cone}} = \frac{1}{3} \pi r^2 (2r) = \frac{2}{3} \pi r^3 \]
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Setting this equal to the given volume of the cone:
\[ \frac{2}{3} \pi r^3 = 12 \]
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Solving for \( r^3 \):
\[ r^3 = 12 \cdot \frac{3}{2 \pi} = \frac{36}{2\pi} = \frac{18}{\pi} \]
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Now, we can find the volume of the hemisphere using its radius \( r \):
\[ V_{\text{hemisphere}} = \frac{2}{3} \pi r^3 = \frac{2}{3} \pi \left( \frac{18}{\pi} \right) = \frac{36}{3} = 12 , \text{m}^3 \]
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Finally, we add the volumes of the cone and hemisphere:
\[ V_{\text{total}} = V_{\text{cone}} + V_{\text{hemisphere}} = 12 + 12 = 24 , \text{m}^3 \]
Thus, the volume of the whole object is 24 m³. Therefore, the correct response is:
24 m3 or 24 m cubed.