$$ \begin{array}{cl} ext { Figure } & ext { Volume } \ -\vee ext { Sphere } & ext { a. } V=\pi r^{2} h \ -\vee ext { Rectangular Solid } & ext { b. } V=l w h \ -\vee ext { Right Circular Cylinder } & ext { c. } V=\frac{4}{3} \pi r^{3}\end{array} $$

Question

$$ \begin{array}{cl}	ext { Figure } & 	ext { Volume } \ -\vee 	ext { Sphere } & 	ext { a. } V=\pi r^{2} h \ -\vee 	ext { Rectangular Solid } & 	ext { b. } V=l w h \ -\vee 	ext { Right Circular Cylinder } & 	ext { c. } V=\frac{4}{3} \pi r^{3}\end{array} $$

UpStudy AI · Accepted Answer

**Step 1. Identify the Known Volume Formulas**

- The volume of a **sphere** is given by  
  $$
  V = \frac{4}{3} \pi r^3
  $$
  
- The volume of a **rectangular solid** (cuboid) is  
  $$
  V = lwh
  $$
  
- The volume of a **right circular cylinder** is  
  $$
  V= \pi r^2 h
  $$

**Step 2. Match the Figures with the Given Formulas**

From the provided table:

- For the **Sphere**, the corresponding formula given is  
  **c. $$V=\frac{4}{3} \pi r^{3}$$**, which matches the known formula for a sphere.

- For the **Rectangular Solid**, the formula is  
  **b. $$V=lwh$$**, which is the correct formula.

- For the **Right Circular Cylinder**, the formula is  
  **a. $$V=\pi r^{2} h$$**, which is indeed the formula for a cylinder.

**Conclusion**

- **Sphere:** Option **c**  
- **Rectangular Solid:** Option **b**  
- **Right Circular Cylinder:** Option **a**
- **Sphere:** c - **Rectangular Solid:** b - **Right Circular Cylinder:** a

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