A high school student builds a rectangular compost bin with a square base. If the volume is 256 cubic feet and the height is four times the side of the base, what is the height?
["How a High School Student Built a Square-Based Compost Bin—With Exactly 256 Cubic Feet of Space", "Ever spotted a teen turning kitchen scraps into garden gold using a simple rectangular bin? This hands-on project—built with a square base and precise measurements—blends STEM learning with eco-conscious living. When the volume is 256 cubic feet and the height reaches four times the base’s side length, what’s the height? The calculation offers more than just numbers—it reveals how everyday math powers real-life sustainability.", "Why This Project is Sparking Interest in the US", "Today’s young builders are drawn to practical, environmental-minded projects that deliver visible results. Composting bins fit perfectly: they’re small enough for backyard use, educational to construct, and deeply rewarding. This type of build aligns with rising interest in sustainable living, DIY skills, and hands-on science—trends gaining traction through social media and school STEM programs. The clear math behind such builds makes them accessible, sparking curiosity and eventual engagement.", "How the Math Works: Finding the Height", "Let the side of the square base be \( x \) feet. Since the base is rectangular with equal sides, the base area is \( x^2 \). Height is given as four times the base’s side, so height = \( 4x \).", "Volume is base area times height: \n\[ \ ext{Volume} = x^2 \cdot 4x = 4x^3 \]", "Set this equal to 256 cubic feet: \n\[ 4x^3 = 256 \]", "Divide both sides by 4: \n\[ x^3 = 64 \]", "Take the cube root: \n\[ x = 4 \]", "Now calculate height: \n\[ \ ext{Height} = 4x = 4 \cdot 4 = 16 \]", "Thus, the bin’s height is 16 feet—a clean, functional design built with math precision.", "Common Questions About This Compost Bin Calculation", "Q: Is there any room left after building this size compost bin? \nA: Yes. At 16 feet tall with a 4-foot square base, it fits well in most backyard spaces"]
