Final answer:
The volume of water in Anju's cone-shaped paper cup, when filled to 3/4 of its height, is approximately 125.66 cm³. This is calculated using the formula for the volume of a cone, with a radius of 4 cm and a height of 7.5 cm.
Step-by-step explanation:
To find the approximate volume of water in Anju's cup, which is shaped like a cone, we need to use the formula for the volume of a cone: V = (1/3)πr^2h, where 'r' is the radius of the base and 'h' is the height of the cone. Since the cup is filled to 3/4 of its height, we will calculate the volume using 3/4 of the total height. The cup has a maximum diameter of 8 cm, so the radius 'r' is half of that, which is 4 cm. The total height 'h' is 10 cm, so the height when the cup is filled to 3/4 is (3/4) * 10 cm = 7.5 cm.
Now, we can calculate the volume: V = (1/3)π(4 cm)^2(7.5 cm) = (1/3)π(16 cm^2)(7.5 cm) = π * 16 cm^2 * 2.5 cm = 40π cm^3. The value of π is approximately 3.1416, so the volume is approximately 40 * 3.1416 cm^3, which is about 125.66 cm^3. Therefore, the volume of water in Anju's cup when filled to 3/4 of its height is approximately 125.66 cm^3.