Prisms and Cylinders — Practice Quiz

A Geometry cheat sheet for Prisms and Cylinders — every key formula with its symbols defined — plus a medium-level practice quiz to test recall.

Practice quiz

1. A rectangular prism has a base area of $25 \text{ cm}^2$ and a height of $10 \text{ cm}$. Using the formula $V = Bh$, what is its volume?

   • $250 \text{ cm}^3$
   • $2500 \text{ cm}^3$
   • $35 \text{ cm}^3$
   • $15 \text{ cm}^3$

   Answer: $250 \text{ cm}^3$

2. A cylinder has a radius of $3 \text{ m}$ and a height of $7 \text{ m}$. Using the formula $V = \pi r^2 h$ and approximating $\pi \approx 3.14$, what is its volume?

   • $197.82 \text{ m}^3$
   • $65.94 \text{ m}^3$
   • $131.88 \text{ m}^3$
   • $220.00 \text{ m}^3$

   Answer: $197.82 \text{ m}^3$

3. A triangular prism has a base area of $12 \text{ in}^2$, a base perimeter of $15 \text{ in}$, and a height of $8 \text{ in}$. Using the formula $SA = 2B + Ph$, what is its surface area?

   • $144 \text{ in}^2$
   • $120 \text{ in}^2$
   • $168 \text{ in}^2$
   • $96 \text{ in}^2$

   Answer: $144 \text{ in}^2$

4. Calculate the surface area of a cylinder with a radius of $4 \text{ cm}$ and a height of $6 \text{ cm}$. Use the formula $SA = 2\pi r(r + h)$ and approximate $\pi \approx 3.14$.

   • $251.2 \text{ cm}^2$
   • $150.72 \text{ cm}^2$
   • $301.44 \text{ cm}^2$
   • $125.6 \text{ cm}^2$

   Answer: $251.2 \text{ cm}^2$

5. A prism has a volume of $180 \text{ cm}^3$ and a base area of $30 \text{ cm}^2$. What is its height, based on the formula $V = Bh$?

   • $6 \text{ cm}$
   • $5400 \text{ cm}$
   • $150 \text{ cm}$
   • $210 \text{ cm}$

   Answer: $6 \text{ cm}$

6. A cylinder has a volume of $300\pi \text{ m}^3$ and a height of $12 \text{ m}$. What is its radius, using the formula $V = \pi r^2 h$?

   • $5 \text{ m}$
   • $25 \text{ m}$
   • $10 \text{ m}$
   • $12.5 \text{ m}$

   Answer: $5 \text{ m}$

7. In the formulas for prism volume ($V = Bh$) and surface area ($SA = 2B + Ph$), what does the variable $B$ represent?

   • Base Area
   • Base Perimeter
   • Body Length
   • Breadth

   Answer: Base Area

8. A rectangular prism has a base area of $50 \text{ cm}^2$ and a height of $8 \text{ cm}$. A cylinder has a radius of $3 \text{ cm}$ and a height of $10 \text{ cm}$. Which shape has a greater volume? Use $\pi \approx 3.14$.

   • The rectangular prism
   • The cylinder
   • They have the same volume
   • Cannot be determined

   Answer: The rectangular prism

9. A cylinder has a surface area of $150\pi \text{ cm}^2$ and a radius of $5 \text{ cm}$. Using the formula $SA = 2\pi r^2 + 2\pi r h$, what is its height?

   • $10 \text{ cm}$
   • $5 \text{ cm}$
   • $15 \text{ cm}$
   • $20 \text{ cm}$

   Answer: $10 \text{ cm}$

10. A cylindrical water tank has a radius of $2 \text{ m}$ and a height of $5 \text{ m}$. If the tank needs to be painted on its entire outer surface (including top and bottom), what is the total area to be painted? Use the formula $SA = 2\pi r(r + h)$ and approximate $\pi \approx 3.14$.

    • $87.92 \text{ m}^2$
    • $62.8 \text{ m}^2$
    • $75.36 \text{ m}^2$
    • $100.48 \text{ m}^2$

    Answer: $87.92 \text{ m}^2$