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Lesson 1: Volumes of Cylinders — Practice Questions

  1. 1. A cylinder has a volume of $628$ cubic feet and a radius of $10$ feet. Using $\pi \approx 3.14$, what is the height of the cylinder in feet? The height is ___ feet.

  2. 2. The volume of a cylindrical container is $320\pi$ cubic inches and its height is $5$ inches. What is the radius of the container in inches? The radius is ___ inches.

  3. 3. A cylinder has volume $V$, radius $r$, and height $h$. Which formula correctly shows how to solve for the radius, $r$?

    • A. $r = \frac{V}{\pi h}$
    • B. $r = \sqrt{\frac{V}{\pi h}}$
    • C. $r = \frac{V^2}{\pi h}$
    • D. $r = \sqrt{V \pi h}$
  4. 4. A cylindrical can has a volume of $75.36 \text{ cm}^3$ and a radius of $2 \text{ cm}$. Using the approximation $\pi \approx 3.14$, find the height of the can. The height is ___ cm.

  5. 5. A cylinder has a volume of $196\pi$ cubic meters and a height of $4$ meters. What is the radius of the cylinder?

    • A. 7 m
    • B. 14 m
    • C. 49 m
    • D. 98 m
  6. 6. A cylindrical soup can has a diameter of 8 cm and is filled with soup to a height of 10 cm. What is the volume of the soup in cubic centimeters? Express your answer in terms of $\pi$. The volume is ___ cm$^3$.

  7. 7. A cylindrical water tank has a radius of 2 meters and a height of 5 meters. If the tank is one-fourth full of water, what is the volume of the water in the tank?

    • A. $20\pi \text{ m}^3$
    • B. $10\pi \text{ m}^3$
    • C. $5\pi \text{ m}^3$
    • D. $2.5\pi \text{ m}^3$
  8. 8. A full cylindrical drum has a radius of 1 ft and a height of 3 ft. Using $1 \text{ ft}^3 \approx 7.48$ gal and $\pi \approx 3.14$, find the volume in gallons, rounded to the nearest whole number. The volume is ___ gallons.

  9. 9. A cylindrical glass is partially filled with water. To find the volume of the water inside, which measurement is needed in addition to the radius of the glass?

    • A. The total height of the glass
    • B. The height of the water in the glass
    • C. The circumference of the glass
    • D. The weight of the glass
  10. 10. A cylindrical grain silo has a diameter of 20 ft and a height of 50 ft. If it is filled to $\frac{3}{5}$ of its capacity, what is the volume of the grain in cubic feet? Express your answer in terms of $\pi$. The volume is ___ ft$^3$.