A big block of ice is in the shape of a perfect cube. As it melts, each edge of the cube is decreasing at the rate of \( 2 \mathrm{~cm} / \mathrm{min} \). The initial size is 20 cm per side. Let \( x \) denote a side length. (e) What formula describes \( x \) as a function of \( t \) ? \( x(t)=20+2 t \) \( x(t)=20 \) \( x(t)=20-2 t \) \( x(t)=-2 t \) (f) If the rate of change of volume with respect to time is asked, what formula couples volume and side length? \( V=\pi x^{2} \) \( V=x^{3} \) \( V=x^{2} \) \( V=6 x^{2} \) (g) If the rate of change of surface area with respect to time is asked, what formula couples surface area and side length? \( S=2 \pi x \) \( S=x^{3} \) \( S=x^{2} \) \( S=6 x^{2} \)

The majestic journey of ice cubes takes us back to ancient civilizations where ice was a luxury. The first recorded use of ice comes from the Chinese, who collected ice from rivers to chill their drinks as far back as 3000 BC! Cool, right? Fast forward to today, whether it's in cocktails or during summer picnics, ice cubes remain a staple for refreshment—showing how a simple phenomenon has stood the test of time! Melting ice isn't just for the sake of refreshing drinks; it’s crucial for scientific exploration too! Glacial melting studies help scientists understand climate change and rising sea levels. Moreover, the principles governing the melting process, such as heat transfer and phase changes, have real-world applications in refrigeration technology and even climate engineering. Isn’t it amazing how studying a cube of ice can lead to breakthroughs in big global challenges?