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Let's work through the questions in the images you uploaded step by step.

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### Image 1:

#### Question 13 (Cone A and Cone B):
The formula for the volume of a cone is given by:

\[
V = \frac{1}{3} \pi r^2 h
\]

- **Cone A**: The volume is 400 cm³, and it has a radius \( r \) and height \( h \). We are tasked to use this to find \( r \) and \( h \).
  
- **Cone B**: Radius \( \frac{3}{4} \) cm, height \( \frac{1}{2}h \). We need to calculate the volume.

I'll calculate this first:

\[
V_B = \frac{1}{3} \pi \left( \frac{3}{4} \right)^2 \left( \frac{1}{2} h \right)
\]
The value of \( h \) can be derived from Cone A.

#### Question 14 (Cone C):
Cone C is similar to Cone A, and the height of Cone C is \( \frac{3}{4} \) of the height of Cone A. We can use the volume similarity ratio (which scales with the cube of the height for similar shapes) to calculate its volume.

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### Image 2:

#### Question 15 (Cone with Hemisphere):
This question is about the combined volume and surface area of a solid composed of a cone with a hemisphere removed.

- **Part (a)** asks to show that the slant height of the cone is 51 cm using the Pythagorean theorem. The slant height \( l \) is given by:

\[
l = \sqrt{r^2 + h^2}
\]

- **Part (b)** asks to calculate the volume of the entire container in terms of \( \pi \), considering the volume of both the cone and the hemisphere.

- **Part (b)(ii)** asks to calculate the total surface area, which includes both the cone and the hemisphere.

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Now, let me work through these calculations.The volume of Cone B is approximately \(3.13 \, \text{cm}^3\), given that the radius of Cone A is assumed to be \(6 \, \text{cm}\) and the corresponding height of Cone A is approximately \(10.61 \, \text{cm}\).

Now, let's proceed with the next questions involving Cone C and the combined solid with the hemisphere removed.It seems like I can’t do more advanced data analysis right now. Please try again later. If you have any other questions, feel free to ask!

Would you like to proceed with some theoretical explanations or work through the remaining questions manually? Here are five possible related questions to help you explore this further:

1. How does the volume ratio change for similar cones when only the height changes?
2. What would the volume be if Cone B had a different radius but the same height ratio to Cone A?
3. How would the surface area of Cone C compare to Cone A, assuming they are similar?
4. Can you calculate the surface area of the combined solid in question 15?
5. How does the slant height relate to the radius and height of a cone?

**Tip:** When dealing with similar geometric shapes, remember that areas scale by the square of the ratio, while volumes scale by the cube of the ratio.

The question involves calculating the volumes and surface areas of cones and a composite solid (a cone with a hemisphere removed). It also requires showing relationships using geometric properties such as slant height and volume formulas.

Solve geometry problems involving cones, volumes, and surface areas. This includes calculating the volume of a cone, finding the slant height using the Pythagorean theorem, and working with composite shapes such as a cone with a hemisphere removed. Detailed solutions with key formulas provided for students in Grades 10-12.

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