A small bottle of Dr. Pepper holds 31.2 cm3 of the delicious drink. For a New Year's Eve party, you need enough juice to fill 6 cone-shaped glasses that have a 4 cm diameter and a 3 cm height. How many full bottles of Dr. Pepper do you need to buy to completely fill the 6 glasses you need?
To find out how many full bottles of Dr. Pepper you need to buy, we first need to calculate the volume of one cone-shaped glass.
The formula to calculate the volume of a cone is:
V = (1/3) * π * r^2 * h
Where:
V = Volume
π = Pi (approximately 3.14159)
r = radius of the base (half of the diameter)
h = height
In this case, the diameter of the glass is given as 4 cm, so the radius would be half of that, which is 2 cm. The height is given as 3 cm.
Calculating the volume of one glass:
V = (1/3) * 3.14159 * (2 cm)^2 * 3 cm
≈ (1/3) * 3.14159 * 4 cm^2 * 3 cm
≈ 12.56637 cm^3
Now, we know the volume of one glass is approximately 12.57 cm^3. To find out how many bottles of Dr. Pepper you need, we divide the total volume required by the volume of one glass.
Total volume required = 6 glasses * 12.57 cm^3
≈ 75.42 cm^3
Next, we can calculate how many full bottles of Dr. Pepper are needed to fill 75.42 cm^3.
Number of bottles needed = 75.42 cm^3 / 31.2 cm^3 (volume of one bottle)
≈ 2.42 bottles
Since you cannot buy a fraction of a bottle, you would need to round up to the nearest whole number. In this case, you would need to buy at least 3 full bottles of Dr. Pepper to completely fill the 6 glasses you need.
the volume of each cone is 1/3 π * 2^2 * 3 = 4π cm^3
So, you will need 24π cm^3 to fill the 6 glasses.
How many bottles is that?