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. The area of the base of a cylinder is 150 square inches. If the volume of the cylinder is \( 1,050 \mathrm{in}^{3} \), what is the height of the cylinder? \( \qquad \) 9. 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. 8. 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 pl . 10. 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. 11. The height of a cylinder is 4 millimeters. The circumference of its base is \( 10 \pi \mathrm{~mm} \). a. What is the radius of the cylinder? Explain. b. Find the volume of the cylinder to the nearest tenth.

Ask by Bryant Montgomery. in the United States
Mar 17,2025

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1. The height of the cylinder is 7 inches. 2. The water tank's capacity is 14.13 cubic meters. 3. The radius of the cylinder is 5 feet. 4. Beau's water bottle holds more water by 63.54 cubic inches. 5. The radius of the cylinder is 5 millimeters, and its volume is 314 cubic millimeters.

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Beyond the Answer

To determine the height of the cylinder when the area of its base is 150 square inches and its volume is 1,050 cubic inches, we can use the formula for the volume of a cylinder: \( V = \text{Base Area} \times \text{Height} \). Rearranging this gives us the height: \( \text{Height} = \frac{V}{\text{Base Area}} = \frac{1050}{150} = 7 \) inches. So, the height of the cylinder is 7 inches! Leann's cylindrical water tank has a diameter of 3 meters, which means the radius is \( \frac{3}{2} = 1.5 \) meters. The volume of a cylinder is given by \( V = \pi r^2 h \). Plugging in the values, we get: \( V = \pi (1.5)^2 (2) \approx 3.14 \times 2.25 \times 2 \approx 14.13 \) cubic meters. So, the water tank can hold approximately 14.13 cubic meters of water!

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