Final answer:
To calculate the volume of water in Anju's cone-shaped cup, use the formula V = 1/3 πr^2h with a radius of 4 cm and a height of 7.5 cm (3/4 the height of the cup). The approximate volume is 126 cm³ after rounding to the nearest cubic centimeter.
Step-by-step explanation:
Volume of Water in Anju's Cone-shaped Paper Cup
To calculate the volume of water in Anju's cone-shaped paper cup, we first need the formula for the volume of a cone: V = 1/3 πr^2h. The diameter of the cup is given as 8 cm, so the radius (r) is half that, which is 4 cm. Anju fills the cup to 3/4 of its height, so the height (h) with water is 3/4 × 10 cm = 7.5 cm. Plugging these values into the formula, we get:
V = 1/3 π × (4 cm)^2 × 7.5 cm
Calculating this, we have:
V ≈ 1/3 × 3.14159 × 16 cm^2 × 7.5 cm
V ≈ 125.663 cm^3
Therefore, the approximate volume of water in Anju's cup when filled to 3/4 of its height is 126 cm³ after rounding to the nearest cubic centimeter.