Question

During practice, the Northwood football team drinks
water from a cylindrical cooler that has a radius of 6
inches and a height of 20 inches. Players use conical
paper cups, as shown below.
If the water cooler is filled completely, can each of the
38 players have two full paper cups of water during
practice? Explain
4.4 in.
O No, because there is enough water in the cooler for
about 3 cups total.
No, because there is enough water in the cooler for
about 59 cups total
5.5 in.
Yes, because there is enough water in the cooler
for about 81 cups total.
Yes, because there is enough water in the cooler
for about 2,261 cups total.

Answer 1

Answer:

The third option (C) Yes, because there is enough water in the cooler for about 81 cups total.Step-by-step explanation:

Answer 2

The radius and height of the cooler of 6 and 20 inches respectively, can

contain approximately only 81 cups, the correct option is therefore;

• Yes, because there is enough water in the cooler for about 81 cups total

How can the correct option be found?

The dimensions of the cooler are;

Radius = 6 inches

Height = 20 inches

The possible dimensions of a cup are;

Diameter = 4.4 inches

Height = 5.5 inches

Required:

If each of the 38 players have 2 paper cups filled with water.

Solution;

The volume of the cooler, V₁, is found as follows;

V₁ = π × 6² × 20 = 720·π

The volume of the cooler, V₁ = 720·π in.³

The volume of the paper cup, V₂, is; $V_2 = \dfrac{1}{3} \times \pi \times \left(\frac{4.4}{2} \right)^2 \times 5.5 = 8\frac{131}{150} \cdot \pi$

The volume of the paper cup, V₂ = $8\frac{131}{150} \cdot \pi$ in.³

The number of cups, n, in the cooler of water is therefore;

• $n = \dfrac{720 \cdot \pi}{8 \frac{131}{150} \cdot \pi } \approx \mathbf{ 81.14}$

The number of cups of water in the cooler ≈ 81 cups

The number of cups required for each of the 38 player to have two full cups is, Cups = 38 × 2 = 76 cups

Given that the water available, (approximately 81 cups) is more than the

number of cups required (76 cups), the correct option is option;

• Yes, because there is enough water in the cooler for about 81 cups total

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