Question

use what youve learned about the volume of cylinders to answer each question below.

1. the area of the base of a cylinder is 150 square inches. if the volume of the cylinder is 1,050 in³, what is the height of the cylinder?
2. the volume of a cylinder is 942 cubic feet. if the height of the cylinder is 12 feet, what is the radius of the cylinder? use 3.14 for pi.
3. leann’s cylindrical water tank in her backyard has a diameter of 3 meters and a height of 2 meters. what is the capacity of the water tank? round to the nearest hundredth.
4. 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.

Explanation:

Step1: Recall cylinder volume formula

The volume of a cylinder is $V = B \times h$, where $B$ is the base area, $h$ is height. Rearranged for height: $h = \frac{V}{B}$

Step2: Substitute values for Q7

Substitute $V=1050\ \text{in}^3$, $B=150\ \text{in}^2$
$h = \frac{1050}{150} = 7$
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Step1: Recall cylinder volume formula

$V = \pi r^2 h$, rearranged for radius: $r = \sqrt{\frac{V}{\pi h}}$

Step2: Substitute values for Q8

Use $\pi=3.14$, $V=942\ \text{ft}^3$, $h=12\ \text{ft}$
$r = \sqrt{\frac{942}{3.14 \times 12}} = \sqrt{\frac{942}{37.68}} = \sqrt{25} = 5$
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Step1: Calculate radius from diameter

Diameter = 3 m, so radius $r = \frac{3}{2} = 1.5$ m

Step2: Calculate tank capacity (volume)

Use $V = \pi r^2 h$, $h=2$ m
$V = \pi \times (1.5)^2 \times 2 = \pi \times 2.25 \times 2 = 4.5\pi \approx 14.14$
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Step1: Calculate Drew's bottle volume

Diameter=3 in, so $r=\frac{3}{2}=1.5$ in, $h=7$ in. $V_D = \pi (1.5)^2 \times 7 = \pi \times 2.25 \times 7 = 15.75\pi \approx 49.46$

Step2: Calculate Beau's bottle volume

Radius=2 in, $h=9$ in. $V_B = \pi (2)^2 \times 9 = \pi \times 4 \times 9 = 36\pi \approx 113.10$

Step3: Compare volumes and find difference

$V_B > V_D$, so Beau's holds more. Difference: $113.10 - 49.46 = 63.64$

Answer:

1. 7 inches
2. 5 feet
3. 14.14 cubic meters
4. Beau's water bottle holds more water; it holds 63.64 cubic inches more.