1. To determine how much confetti can fit in the cone-shaped hat without overflowing, we need to know the volume of the hat. The formula for the volume of a cone is:
V = (1/3)πr^2h
where V is the volume, r is the radius of the circular base of the cone, h is the height of the cone, and π is approximately equal to 3.14.
We will need to know the radius and height of the cone hat to calculate its volume. Once we have the volume, we can fill the cone with confetti up to its brim without overflowing.
Let's assume that the cone hat has a radius of 5 cm and a height of 15 cm. Then, using the formula above, we can calculate the volume of the cone hat:
V = (1/3)πr^2h
V = (1/3)π(5 cm)^2(15 cm)
V ≈ 392.7 cubic cm
Therefore, Brooke can place approximately 392.7 cubic cm of confetti in the cone-shaped hat without it overflowing. Rounded to the nearest cubic centimeter, the answer is 393 cubic cm.
2. To calculate the volume of the snow globe, we need to use the formula for the volume of a sphere:
V = (4/3)πr^3
where V is the volume, r is the radius of the sphere, and π is approximately equal to 3.14.
The dimensions given in the problem are the length and width, so we need to determine the radius of the sphere. We can do this by dividing the length by 2, since the diameter of the sphere is equal to the length of the rectangular base.
r = 7 inches / 2 = 3.5 inches
Now we can use the formula for the volume of a sphere to calculate the volume of the snow globe:
V = (4/3)πr^3
V = (4/3)π(3.5 inches)^3
V ≈ 179.6 cubic inches
Therefore, the volume of the snow globe is approximately 179.6 cubic inches. Rounded to the nearest cubic centimeter, the answer is 2943 cubic cm.
3. To calculate the volume of the billiard ball, we need to use the formula for the volume of a sphere:
V = (4/3)πr^3
where V is the volume, r is the radius of the sphere, and π is approximately equal to 3.14.
The diameter of the billiard ball is given as 61.5 mm, so we can find the radius by dividing the diameter by 2:
r = 61.5 mm / 2 = 30.75 mm
Now we can use the formula for the volume of a sphere to calculate the volume of the billiard ball:
V = (4/3)πr^3
V = (4/3)π(30.75 mm)^3
V ≈ 92543.6 cubic mm
Therefore, the volume of the billiard ball is approximately 92543.6 cubic mm. Rounded to the nearest cubic centimeter, the answer is 92,544 cubic mm.