If Bill gets a full scoop of frozen yogurt in a cone, with the scoop being a
perfect sphere with a diameter of 5 cm, then the yogurt would NOT fill up
the inside of the cone if you pushed it down into the cone.
5cm
11 cm
(2 points)
True: volume of the yogurt is more than the volume of the cone
False: volume of the cone is less than the volume of the yogurt
True: volume of the yogurt is less than the volume of the cone
False: volume of the cone is more than the volume of the yogurt
True: volume of the yogurt is less than the volume of the cone
To calculate the volume of a cone, you use the formula V = (1/3)πr^2h, where r is the radius of the base of the cone and h is the height of the cone. In this case, the cone has a diameter of 11 cm, so the radius is 5.5 cm and the height is 5 cm. Plugging these values into the formula, the volume of the cone is approximately 96.19 cubic cm.
The volume of a sphere can be calculated using the formula V = (4/3)πr^3. Plugging in the radius of 2.5 cm (half of the diameter of 5 cm), the volume of the sphere is approximately 65.45 cubic cm.
Since the volume of the yogurt (sphere) is less than the volume of the cone, the statement is true.