To find the volume of the solid object composed of a cone and a hemisphere, we need to calculate the volumes of both the cone and the hemisphere separately and then add them together.

### Volume of the Cone
The formula for the volume of a cone is:
\[ V_{\text{cone}} = \frac{1}{3} \pi r^2 h \]

We already know the radius \( r = 7 \, \text{cm} \) and the height \( h = 24 \, \text{cm} \) from our previous calculations.

\[ V_{\text{cone}} = \frac{1}{3} \pi (7)^2 (24) \]
\[ V_{\text{cone}} = \frac{1}{3} \pi (49) (24) \]
\[ V_{\text{cone}} = \frac{1}{3} \pi (1176) \]
\[ V_{\text{cone}} = 392 \pi \]

### Volume of the Hemisphere
The formula for the volume of a hemisphere is:
\[ V_{\text{hemisphere}} = \frac{2}{3} \pi r^3 \]

We already know the radius \( r = 7 \, \text{cm} \).

\[ V_{\text{hemisphere}} = \frac{2}{3} \pi (7)^3 \]
\[ V_{\text{hemisphere}} = \frac{2}{3} \pi (343) \]
\[ V_{\text{hemisphere}} = \frac{2}{3} \pi (343) \]
\[ V_{\text{hemisphere}} = \frac{686}{3} \pi \]

### Total Volume of the Solid
The total volume is the sum of the volumes of the cone and the hemisphere.

\[ V_{\text{total}} = V_{\text{cone}} + V_{\text{hemisphere}} \]
\[ V_{\text{total}} = 392 \pi + \frac{686}{3} \pi \]
\[ V_{\text{total}} = \pi \left( 392 + \frac{686}{3} \right) \]
\[ V_{\text{total}} = \pi \left( \frac{1176 + 686}{3} \right) \]
\[ V_{\text{total}} = \pi \left( \frac{1862}{3} \right) \]
\[ V_{\text{total}} = \frac{1862}{3} \pi \]

Approximating \(\pi\) as 3.14:

\[ V_{\text{total}} \approx \frac{1862}{3} \times 3.14 \]
\[ V_{\text{total}} \approx 620.67 \times 3.14 \]
\[ V_{\text{total}} \approx 1948.90 \, \text{cm}^3 \]

### Summary
The volume of the solid object is approximately \(1948.90 \, \text{cm}^3\).

Would you like more details or have any questions?

Here are five related questions you might find useful:
1. How do you find the volume of a cylinder?
2. What is the surface area of a sphere?
3. How do you calculate the volume of a rectangular prism?
4. What is the formula for the volume of a pyramid?
5. How do you find the height of a cone if you know its volume and radius?

**Tip:** When working with combined solids, always handle each shape separately to ensure accuracy, then sum their respective properties as needed.

Learn how to calculate the volume of a solid object composed of a cone and a hemisphere step-by-step. This problem involves finding the volumes of both shapes separately using their respective formulas and then summing them up. Suitable for high school students studying geometry and solid geometry.

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