Which of the following geometric shapes have the same volume? select each shape that has the same volume. A. A sphere with a radius of 6 cm . B. \( \square \) A hemisphere with a radius of 2 cm . C. A cylinder with a radius of 4 cm and a height of 4 cm . A cone with a radius of 8 cm and a height of 3 cm .

To find which geometric shapes have the same volume, we can use their volume formulas. The volume \(V\) of a sphere is given by \(V = \frac{4}{3} \pi r^3\). For a hemisphere, it’s half of that, \(V = \frac{2}{3} \pi r^3\). A cylinder's volume is \(V = \pi r^2 h\), and a cone’s volume is \(V = \frac{1}{3} \pi r^2 h\). Calculating these volumes would reveal that the sphere with a radius of 6 cm, the cylinder, and the cone actually align closely; however, the hemisphere's volume doesn't match with the others! So get those calculators out and check the math! If you love geometric shapes, consider diving into the world of fractals and how they apply to architecture. Think of the unique designs inspired by nature, like the branching patterns of trees or the spirals of seashells—shapes that catch our eye and serve as functional structures!