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Quizzes > Mathematics > Geometry

Test Your Surface Area & Volume Skills: Prisms & Cylinders

Ready for prism volume practice and a cylinder surface area test? Dive in!

Difficulty: Moderate
2-5mins
Learning OutcomesCheat Sheet
Paper art depicting prisms and cylinders for a geometry quiz on golden yellow background

This surface area and volume quiz helps you practice calculations for prisms and cylinders so you can work faster and make fewer errors. Work through mixed problems and cylinder volume questions , get instant feedback, and spot gaps before a test.

What is the volume of a rectangular prism with length 5 units, width 3 units, and height 4 units?
40 cubic units
24 cubic units
60 cubic units
80 cubic units
The volume of a rectangular prism is found by multiplying length × width × height. Here that is 5 × 3 × 4 = 60 cubic units. This formula applies to all right rectangular prisms. For more details see .
What is the total surface area of a cylinder with radius 2 units and height 5 units?
40? square units
14? square units
28? square units
20? square units
The total surface area of a closed cylinder is 2?r(h + r). Substituting r=2 and h=5 gives 2?·2·(5+2) = 28?. Always include both the curved surface and the two bases. See for more.
Calculate the volume of a cylinder with radius 3 units and height 10 units.
30? cubic units
90? cubic units
180? cubic units
120? cubic units
Volume of a cylinder is ?r²h. Here r=3, h=10, so ?·3²·10 = 90? cubic units. This is the standard volume formula for right circular cylinders. More examples at .
A triangular prism has a triangular base perimeter of 12 units and a length of 7 units. What is its lateral surface area?
60 square units
84 square units
27 square units
100 square units
Lateral surface area of a prism equals the perimeter of its base times its length: LSA = P × l. Here, P=12 and l=7, so LSA = 84. This excludes the areas of the two triangular ends. See .
What is the total surface area of a cube with edge length 4 units?
64 square units
48 square units
96 square units
32 square units
A cube has 6 faces, each a square of side 4 units, so area per face is 16. Total surface area is 6 × 16 = 96. This applies only to cubes where all edges are equal. See .
Find the volume of a right prism with base area 15 square units and height 8 units.
64 cubic units
23 cubic units
120 cubic units
30 cubic units
Volume of any prism is base area × height. Here that is 15 × 8 = 120 cubic units. This holds for triangular, rectangular, or any prism shape. For further reading see .
A cylinder is inscribed in a cube of side length 10 units. What is the volume of this cylinder?
125? cubic units
100? cubic units
250? cubic units
500? cubic units
An inscribed cylinder in a cube has diameter equal to the cube's side (10), so radius = 5. Height is also 10. Volume = ?r²h = ?·5²·10 = 250?. More on inscribed solids at .
What is the volume of a right prism whose base is an equilateral triangle with side length 6 units and whose prism height is 10 units?
54?3 cubic units
36?3 cubic units
72?3 cubic units
90?3 cubic units
Base area = (?3/4)·6² = 9?3. Prism volume = base area × height = 9?3 × 10 = 90?3. Equilateral triangle area formula is essential here. See .
A cylindrical water tank has a radius of 3 meters and height of 12 meters. If only the curved surface and the top are painted (base excluded), what area is painted?
90? square meters
81? square meters
63? square meters
72? square meters
Painted area = lateral area + top area = 2?rh + ?r² = 2?·3·12 + ?·3² = 72? + 9? = 81?. The base is not painted, so it's excluded. Check .
Find the volume of a regular hexagonal prism with base edge 4 units and prism height 12 units.
288?3 cubic units
192?3 cubic units
432?3 cubic units
144?3 cubic units
A regular hexagon area = (3?3/2)·s² = (3?3/2)·16 = 24?3. Prism volume = base area × height = 24?3 × 12 = 288?3. This uses the formula for regular hexagon area. See .
A cylinder has a volume of 882? cubic units and a height of 7 units. What is its radius?
?126 units
?63 units
?42 units
9 units
Volume = ?r²h, so ?r²·7 = 882? ? r² = 882/7 = 126 ? r = ?126. Always isolate r² and then take the square root. More on solving for radius at .
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Study Outcomes

  1. Calculate Prism Surface Area -

    Use given dimensions to compute the total and lateral surface area of rectangular and triangular prisms with accuracy.

  2. Compute Prism Volume -

    Apply volume formulas to determine the space inside various prisms, reinforcing the steps for finding the base area and height.

  3. Calculate Cylinder Surface Area -

    Determine the curved and total surface area of cylinders using radius and height in both theoretical and applied problems.

  4. Compute Cylinder Volume -

    Use the formula πr²h to calculate the volume of cylinders, ensuring precise use of constants and units in each question.

  5. Interpret Real-World Geometry Problems -

    Translate everyday scenarios into geometry questions by identifying relevant shapes and dimensions for prisms and cylinders.

  6. Evaluate and Compare Results -

    Analyze and cross-check solutions for accuracy, then compare outcomes between different solid shapes to deepen understanding.

Cheat Sheet

  1. Prism Volume Fundamentals -

    The volume of any prism is V = B × h, where B is the area of the base and h is the height. For a rectangular prism, use B = length × width to quickly calculate V and boost your prism volume practice. Regularly revisiting this formula sharpens your speed for every surface area and volume quiz you tackle.

  2. Prism Surface Area Formula -

    To calculate prism surface area, use SA = 2B + Ph, where P is the perimeter of the base and B is the base area. A handy mnemonic is "Two Bases Plus Perimeter Height" to lock in the structure of this formula. Practicing calculate prism surface area examples from university sites like MIT OpenCourseWare solidifies your grasp.

  3. Cylinder Volume Principles -

    The volume of a cylinder is V = πr²h, with r as the radius and h as the height - perfect for everyday volume of cylinder problems like finding how much water fits in a tank. Plug in the values, and you'll see how quickly πr²h becomes second nature during prism volume practice sessions. Trusted resources such as Khan Academy offer guided exercises to reinforce this key formula.

  4. Cylinder Surface Area Deep Dive -

    The total surface area of a cylinder is SA = 2πr² + 2πrh, combining the areas of two circles and the side rectangle. Visualizing how the lateral surface "unrolls" into a rectangle of width 2πr and height h is a great trick for your cylinder surface area test. Reference materials from Wolfram MathWorld provide clear diagrams and examples to cement this concept.

  5. Quiz Strategy and Formula Recall -

    When tackling a geometry quiz online, sketch nets of prisms and cylinders to visualize which faces contribute to surface area or volume. Keep a small formula sheet or mnemonic flashcards - like "B × h for volume, La + 2B for area" - to reduce stress and boost confidence. Incorporating timed drills from official university repositories ensures you're quiz-ready for any surface area and volume quiz scenario.

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