First, let's calculate the volume of each cone-shaped cup.
The formula for the volume of a cone is V = (1/3)πr^2h, where r is the radius and h is the height.
Given that the diameter of the cone-shaped cup is 7 cm (so the radius is 3.5 cm) and the height is 10 cm:
V = (1/3)π(3.5)^2(10) = 38.48 cm^3
Now, let's calculate the total volume needed for 900 servings:
Total Volume = 900 servings x 38.48 cm^3 = 34632 cm^3
Next, let's calculate the volume of one can of sports drink:
V = π(7.5)^2(30) = 5309.29 cm^3
Now, let's find out how many cans Larissa needs to purchase:
Number of cans = Total Volume needed / Volume of one can
Number of cans = 34632 cm^3 / 5309.29 cm^3 ≈ 6.52
Since Larissa cannot purchase a fraction of a can, she will need to purchase ceil(6.52) = 7 cans of the sports drink to have enough for 900 servings. So, the minimum number of cans Larissa should purchase is 7.
Larissa is helping plan the campus Spring Fling, which is a variety of fun competitions, games, and activities the last day of school. It is held outside, so she is going to have a booth with a sports drink served in cone-shaped paper cups. The cone-shaped paper cups have a diameter of 7 cm and a height of 12 cm, but Larissa is going to use a height of 10 cm when calculating the volume of each cup because she is not going to fill the cup to the top.
Larissa is able to purchase the sports drink in economy cans that are cylindrical, with a diameter of 15 cm and a height of 30 cm. The cans are completely full.
Larissa wants to purchase enough cans of the sports drink to have 900 servings of the sports drink. A serving is the volume Larissa calculated for the cone-shaped cup.
What is the minimum number of cans of the sports drink that Larissa should purchase?
1 answer
1 answer