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Quizzes > High School Quizzes > Mathematics

Surface Area & Volume Practice Quiz

Ace Your Unit Test with Review and Worksheets

Difficulty: Moderate
Grade: Grade 8
Study OutcomesCheat Sheet
Paper art representing a trivia quiz on surface area and volume for high school geometry exam prep.

What is the formula for the volume of a rectangular prism?
Length + Width + Height
Length × Width × Height
2(Length + Width + Height)
Length × Width + Height
The volume of a rectangular prism is found by multiplying its length, width, and height together. This product gives the total number of cubic units contained in the prism.
What is the formula for the surface area of a cube with edge length a?
6a²
4a²
a²
3a²
A cube has six congruent square faces, and each face has an area of a². Multiplying the area of one face by 6 gives the total surface area.
What is the formula for the volume of a cylinder with radius r and height h?
πr²h
2πrh
πrh
πr²h/2
The volume of a cylinder is calculated by multiplying the area of its circular base (πr²) by its height h. This formula determines the capacity of the cylinder.
What is the formula for the surface area of a sphere with radius r?
4πr²
2πr²
πr²
8πr²
The surface area of a sphere is given by the formula 4πr², which accounts for the continuous curved surface. This formula is derived by integrating over the sphere.
What is the formula for the lateral surface area of a cylinder with radius r and height h?
2πrh
πrh
πr²h
2πr²
The lateral surface area of a cylinder is calculated by multiplying the circumference of the base (2πr) by the height (h). This gives the area of the side surface, excluding the top and bottom.
What is the volume of a cube with edge length 5 units?
125
25
75
100
The volume of a cube is found by raising the edge length to the third power. In this case, 5³ equals 125 cubic units.
What is the total surface area of a rectangular prism with length 3 units, width 4 units, and height 5 units?
94
80
100
108
The total surface area is calculated by the formula 2(lw + lh + wh). Substituting the given dimensions yields 2(12 + 15 + 20) which simplifies to 94 square units.
A sphere has a volume of 36π cubic units. What is its radius?
3
4
6
9
Using the sphere volume formula (4/3)πr³ = 36π, we solve for r³ to get 27, and the cube root of 27 is 3. Thus, the radius is 3 units.
What is the volume of a cone with a base radius of 3 units and a height of 4 units?
12π
36π
9π
15π
The volume of a cone is given by the formula (1/3)πr²h. Substituting r = 3 and h = 4 yields (1/3)π(9)(4) which simplifies to 12π.
What is the total surface area of a cylinder with a radius of 3 units and a height of 5 units?
48π
24π
40π
56π
The total surface area of a cylinder is calculated as 2πr(h + r). For r = 3 and h = 5, the formula becomes 2π × 3 × (5 + 3) which equals 48π.
Which formula represents the lateral surface area of a square pyramid with a base side length s and slant height l?
2sl
sl
4sl
s + l
For a square pyramid, the lateral surface area is calculated as 1/2 times the perimeter of the base times the slant height. Since the perimeter is 4s, the formula simplifies to 2sl.
What is the volume of a prism with a base area of 10 square units and a height of 6 units?
60
16
30
120
The volume of a prism is found by multiplying the base area by the height. Here, 10 × 6 equals 60 cubic units.
If all dimensions of a geometric solid are doubled, by what factor does its volume increase?
8
4
2
16
Doubling each dimension of a solid increases its volume by a factor of 2³, which is 8. This is due to the cubic relationship between linear dimensions and volume.
If the radius of a sphere is tripled, by what factor does its surface area increase?
9
3
6
27
Since the surface area of a sphere is proportional to the square of its radius, tripling the radius increases the surface area by 3², which is 9 times.
If the volume of a cube is 64 cubic units, what is the length of one of its edges?
4
8
16
32
The volume of a cube is given by edge³. Thus, if edge³ equals 64, the edge length is the cube root of 64, which is 4.
A right cylinder has a volume of 150π cubic units and a height of 10 units. What is its radius?
√15
√10
√20
15
Using the cylinder volume formula, V = πr²h, we substitute the given values to get r² = 150/10, which simplifies to 15. The radius is therefore √15.
A sphere and a cylinder have equal volumes. If the sphere has a radius of 3 units and the cylinder has the same base radius, what must be the height of the cylinder?
4
6
3
9
The volume of the sphere is (4/3)π(3³) which equals 36π. Setting the cylinder's volume, π(3²)h, equal to 36π leads to h = 4.
A cone and a cylinder share the same base and height. What is the ratio of the volume of the cone to that of the cylinder?
1/3
1/2
1
3
The volume of a cone is always one-third that of a cylinder with the same base area and height. Therefore, the ratio is 1/3.
A composite solid consists of a cube with a side length of 4 units and a hemisphere on top of the cube with a radius of 4 units. What is the total volume of the composite solid (express your answer in terms of π)?
64 + (128/3)π
64 + (64/3)π
64 + 128π
(64/3) + 128π
The cube has a volume of 4³ = 64 cubic units. The hemisphere's volume is half that of a sphere, calculated as (1/2) × (4/3)π(4³) which simplifies to (128/3)π. Their sum gives the total volume.
What is the volume of a pyramid with a square base of side length 6 units and a height of 9 units?
108
162
54
216
The volume of a pyramid is calculated using the formula 1/3 × base area × height. For a square base with side 6, the area is 36, and 1/3 × 36 × 9 equals 108 cubic units.
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Study Outcomes

  1. Calculate the surface areas of a variety of geometric solids using standard formulas.
  2. Determine the volumes of different shapes through applied problem-solving techniques.
  3. Analyze geometric problems to identify and extract key information for computations.
  4. Apply algebraic methods to manipulate formulas and verify surface area and volume results.

Surface Area & Volume Review Cheat Sheet

  1. Master 3D Shape Formulas - Become BFFs with surface area and volume equations for cubes, cylinders, cones, and spheres. For instance, cylinder volume is πr²h, where r is radius and h is height. Armed with these killer formulas, you'll conquer any geometry challenge in record time! Teachoo: Surface Area & Volume Formulas
  2. Break Down Composite Shapes - Tackle complex solids by slicing them into simpler parts, then sum their individual areas and volumes. This playful "lego" approach not only simplifies problems but also sharpens logical thinking. Soon, you'll be piecing together shapes like a geometry architect! GeeksforGeeks: Practice Problems
  3. Spot the Area-Volume Relationship - Notice that as a shape grows, its volume balloons faster than its surface area. Understanding this quirky ratio is key for real-life scenarios like packaging design or heat management. Once you've wrapped your head around this concept, you'll see geometry's hidden magic. Wikipedia: Surface Area
  4. Master Units Like a Pro - Surface area uses square units (e.g., cm²) while volume uses cubic units (e.g., cm³), so mixing them up can trip you up fast. Practice converting between units to avoid calculation calamities. With seamless unit mastery, your answers will always hit the mark! GeeksforGeeks: Unit Practice
  5. Apply to Real-World Problems - Figure out how much paint covers a wall or the capacity of a juice bottle by plugging formulas into practical scenarios. This hands-on method bridges the gap between theory and everyday life. Next time you meal-prep or DIY, you'll wield geometry like a secret superpower! GeeksforGeeks: Applications
  6. Use Mnemonics for Quick Recall - Memorize formulas with fun tags like "V = Bh" to remember that prism volume equals Base area times Height. Whip out catchy rhymes or acronyms to cement these formulas in your brain. During quizzes, these mnemonic sidekicks will be your trusty allies. Quizlet Flashcards
  7. Convert Units on the Fly - Bonus points for seamless shifts between mm³, cm³, m³ and their square counterparts, especially when test questions throw curveballs. Regular practice ensures you're not stuck Googling conversions mid-exam. Soon, unit hopping will feel like a breeze! GeeksforGeeks: Unit Conversion
  8. Lateral vs. Total Surface Area - Learn the difference: lateral area covers the "sides" (like the curved part of a cylinder) while total includes all faces. Knowing when to use each formula will save you from calculation slip-ups. Embrace this distinction and watch your accuracy skyrocket! Teachoo: Curved vs. Total Area
  9. Dive into Formula Derivations - Unravel how formulas spring from basic principles - like integrating circles to get sphere volume - to deepen your comprehension. This detective work equips you to adapt formulas for novel shapes or tricky variants. Plus, connecting the dots is a fun math adventure! Wikipedia: Formula Derivation
  10. Practice, Practice, Practice! - The secret sauce to geometry greatness is exposure to diverse problems, from textbook exercises to online quizzes. Aim for at least a handful of new questions daily to build confidence and speed. Before you know it, surface area and volume will be your playground! IXL: Surface Area & Volume Review
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