(b) Find the diameter of its great circle. (c) How many outer layer of the sphere are there? Find it. (a) Find the radius of a sphere whose surface area is equal to the area of a circle with diameter 5.6 (b) Find the volume of a sphere whose area of the great circle is equal to the curved surf area of a hemi-sphere with circumference of great circle 44 cm . c) Calculate the volume of a sphere whose surfale

Certainly! Let's address each part of your question step by step. From your message, it appears there are multiple subparts (a), (b), and (c). I'll interpret and solve each one based on the information provided. --- ### **Part (a): Find the radius of a sphere whose surface area is equal to the area of a circle with diameter 5.6** **Given:** - Diameter of the circle, \( D_c = 5.6 \) units - Radius of the circle, \( r_c = \frac{D_c}{2} = 2.8 \) units **Area of the Circle:** \[ A_c = \pi r_c^2 = \pi (2.8)^2 = \pi \times 7.84 \] **Surface Area of the Sphere:** \[ A_s = 4\pi r_s^2 \] **Setting the Surface Area of the Sphere equal to the Area of the Circle:** \[ 4\pi r_s^2 = \pi \times 7.84 \] **Solving for \( r_s \):** \[ 4 r_s^2 = 7.84 \\ r_s^2 = \frac{7.84}{4} = 1.96 \\ r_s = \sqrt{1.96} = 1.4 \text{ units} \] **Answer:** The radius of the sphere is **1.4 units**. --- ### **Part (b): Find the volume of a sphere whose area of the great circle is equal to the curved surface area of a hemisphere with a circumference of the great circle \(44 \text{ cm}\).** **Given:** - Circumference of the great circle of the hemisphere, \( C = 44 \text{ cm} \) **Finding the Radius of the Hemisphere (\( R_h \)):** \[ C = 2\pi R_h \\ R_h = \frac{C}{2\pi} = \frac{44}{2\pi} = \frac{22}{\pi} \text{ cm} \approx 7 \text{ cm} \] **Curved Surface Area of the Hemisphere (\( A_{hemi} \)):** \[ A_{hemi} = 2\pi R_h^2 = 2\pi \left(\frac{22}{\pi}\right)^2 = 2\pi \times \frac{484}{\pi^2} = \frac{968}{\pi} \text{ cm}^2 \] **Area of the Great Circle of the Sphere (\( A_{gc} \)):** \[ A_{gc} = \pi r^2 \] **Setting \( A_{gc} = A_{hemi} \):** \[ \pi r^2 = \frac{968}{\pi} \\ r^2 = \frac{968}{\pi^2} \\ r = \frac{\sqrt{968}}{\pi} \approx \frac{31.11}{3.1416} \approx 9.9 \text{ cm} \] **Volume of the Sphere (\( V \)):** \[ V = \frac{4}{3}\pi r^3 \\ V = \frac{4}{3}\pi (9.9)^3 \approx \frac{4}{3}\pi \times 970 \approx 4060 \text{ cm}^3 \] **Answer:** The volume of the sphere is approximately **4060 cm³**. --- ### **Part (c): How many outer layers of the sphere are there? Find it.** **Clarification Needed:** The term "outer layer of the sphere" is a bit ambiguous in this context. It could refer to several concepts, such as: 1. **Concentric Layers/Shells:** If the sphere is composed of multiple concentric shells, the number of layers would depend on specific details about each shell's thickness. 2. **Surface Layers in Material Science:** In some contexts, especially in material science or geology, "layers" might refer to different strata or material compositions. 3. **Electron Shells (in Atomic Physics):** If relating to atomic models, electron shells could be considered, but this seems less likely given the geometric context of previous parts. **Recommendation:** Could you please provide more details or clarify what you mean by "outer layer of the sphere"? This will help in providing an accurate and helpful answer. --- If you have any further details or additional questions, feel free to share them!