Anju's office uses paper cups shaped like cones to serve water. Each cup has a maximum diameter of 8 cm and a height of 10 cm . Anju fills the cup to \( \frac{3}{4} \) of its height to prevent spills. What is the approximate volume of water in Anju's cup? Round to the nearest cubic centimeter.

To find the volume of water in Anju's cup, we first need to calculate the volume of the cone-shaped cup. The formula for the volume \( V \) of a cone is: \[ V = \frac{1}{3} \pi r^2 h \] Given that the diameter of the cup is 8 cm, the radius \( r \) is: \[ r = \frac{8}{2} = 4 \, \text{cm} \] The height \( h \) of the cup is 10 cm. Plugging in the values: \[ V = \frac{1}{3} \pi (4^2)(10) = \frac{1}{3} \pi (16)(10) = \frac{160}{3} \pi \, \approx 167.55 \, \text{cm}^3 \] Since Anju fills the cup to \( \frac{3}{4} \) of its height, the height of water in the cup is: \[ h_{water} = \frac{3}{4} \times 10 = 7.5 \, \text{cm} \] Now, we calculate the volume of water: \[ V_{water} = \frac{1}{3} \pi (4^2)(7.5) = \frac{1}{3} \pi (16)(7.5) = \frac{120}{3} \pi \, \approx 125.66 \, \text{cm}^3 \] Rounding to the nearest cubic centimeter, the volume of water in Anju's cup is approximately: \[ \boxed{126} \, \text{cm}^3 \] Fun fact: Did you know that the cone shape is particularly efficient for holding liquids? That's why we see this design in many places, from fancy desserts to practical water cups like Anju's. Plus, the geometry makes it easy to stack, reducing space when storing! Real-world application: Cone cups are often used in schools, offices, and festivals for quick hydration solutions. They’re not just for water; you could sip juice or soda too! The nice point about cones is that they can limit spills while providing a fun sipping experience.