Drew and Beau each brought a cylindrical water bottle to football practice. Drew's water bottle has a diameter of 3 inches and a height of 7 inches. Beau's water bottle has a radius of 2 inches and a height of 9 inches. Whose water bottle holds more water and how much more does it hold? Round to the nearest hundredth.

Question

UpStudy AI · Accepted Answer

Let the volume of a cylinder be given by  
$$
V = \pi r^2 h.
$$

**Step 1: Compute the volume of Drew's water bottle.**

Drew's water bottle has a diameter of 3 inches, so the radius is  
$$
r_D = \frac{3}{2} = 1.5 \text{ inches}.
$$  
It has a height of  
$$
h_D = 7 \text{ inches}.
$$  
Thus, the volume is  
$$
V_D = \pi (1.5)^2 (7) = \pi (2.25)(7) = 15.75\pi \text{ cubic inches}.
$$

**Step 2: Compute the volume of Beau's water bottle.**

Beau's water bottle has a radius of  
$$
r_B = 2 \text{ inches},
$$  
and a height of  
$$
h_B = 9 \text{ inches}.
$$  
Thus, the volume is  
$$
V_B = \pi (2)^2 (9) = \pi (4)(9) = 36\pi \text{ cubic inches}.
$$

**Step 3: Determine whose bottle holds more water and by how much.**

Beau's bottle holds  
$$
36\pi - 15.75\pi = 20.25\pi \text{ cubic inches more water}.
$$

**Step 4: Calculate the numerical value and round to the nearest hundredth.**

Using $$\pi \approx 3.14159$$, we have  
$$
20.25\pi \approx 20.25 \times 3.14159 \approx 63.62 \text{ cubic inches}.
$$

Thus, Beau's water bottle holds approximately $$63.62$$ cubic inches more water than Drew's water bottle.
Beau's water bottle holds approximately 63.62 cubic inches more water than Drew's.

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