Loading...

About Volume & Surface Area — Class 8 IB

Calculate volume and surface area of prisms, cylinders, and composite solids. This topic is part of the IB Class 8 mathematics syllabus (chapter: Unit 7). On this page you can practice 60 questions across three difficulty levels — 20 easy, 20 medium, and 20 hard — each with a visual step-by-step solution, plus a timed 35-question mastery test with a live leaderboard. Worked examples and sample questions from the topic are below.

Volume & Surface Area — solved examples for Class 8 IB

Example 1easy

Find the volume of a rectangular prism with length 5 cm, width 3 cm, and height 4 cm.
  1. A)30 cm³
  2. B)47 cm³
  3. C)60 cm³
  4. D)94 cm³

Step-by-step solution

  1. V = lwh
    5×3×4=60 cm35 \times 3 \times 4 = 60 \text{ cm}^3

Answer: 60 cm³

Example 2medium

A cylinder has radius 7 cm and height 10 cm. Find its volume in terms of \(\pi\).
  1. A)\(490\pi\) cm³
  2. B)\(140\pi\) cm³
  3. C)\(70\pi\) cm³
  4. D)\(980\pi\) cm³

Step-by-step solution

  1. V = πr²h
    π×49×10=490π cm3\pi \times 49 \times 10 = 490\pi \text{ cm}^3

Answer: \(490\pi\) cm³

Example 3hard

A composite solid is made of a cylinder (r = 3, h = 8) with a hemisphere (r = 3) on top. Find the total volume in terms of \(\pi\).
  1. A)\(72\pi + 18\pi\) cm³
  2. B)\(90\pi\) cm³
  3. C)\(72\pi\) cm³
  4. D)\(54\pi\) cm³

Step-by-step solution

  1. Cylinder: π(9)(8) = 72π.
    Hemisphere: 23π(27)=18π\text{Hemisphere: } \frac{2}{3}\pi(27) = 18\pi
  2. Total = 72π + 18π = 90π cm³.

Answer: \(90\pi\) cm³

Practice questions on Volume & Surface Area

  1. Q1.easy

    Find the surface area of a cube with side length 4 cm.
    1. A)48 cm²
    2. B)64 cm²
    3. C)96 cm²
    4. D)16 cm²
    Show answer

    Answer: 96 cm²

    Hint: A cube has 6 equal faces.

  2. Q2.easy

    What is the volume of a cube with side 3 cm?
    1. A)9 cm³
    2. B)18 cm³
    3. C)27 cm³
    4. D)54 cm³
    Show answer

    Answer: 27 cm³

    Hint: Volume of a cube = s³.

  3. Q3.easy

    Find the volume of a cylinder with radius 3 cm and height 10 cm. (Use \(\pi \approx 3.14\))
    1. A)94.2 cm³
    2. B)188.4 cm³
    3. C)282.6 cm³
    4. D)314 cm³
    Show answer

    Answer: 282.6 cm³

    Hint: Volume = πr²h.

  4. Q4.medium

    Find the total surface area of a cylinder with r = 3 cm and h = 8 cm in terms of \(\pi\).
    1. A)\(48\pi\) cm²
    2. B)\(66\pi\) cm²
    3. C)\(72\pi\) cm²
    4. D)\(54\pi\) cm²
    Show answer

    Answer: \(66\pi\) cm²

    Hint: TSA = 2πr(r + h).

  5. Q5.medium

    A triangular prism has a right-angled triangular cross section with legs 3 cm and 4 cm. The prism is 12 cm long. Find its volume.
    1. A)36 cm³
    2. B)48 cm³
    3. C)72 cm³
    4. D)144 cm³
    Show answer

    Answer: 72 cm³

    Hint: Area of right triangle = ½ × base × height.

  6. Q6.medium

    A swimming pool is 25 m long, 10 m wide, and 2 m deep. How many litres of water does it hold? (1 m³ = 1000 L)
    1. A)500 L
    2. B)5000 L
    3. C)50,000 L
    4. D)500,000 L
    Show answer

    Answer: 500,000 L

    Hint: Volume in m³ × 1000 = litres.

  7. Q7.hard

    A cylinder has the same radius and height as a cone. If the cone's volume is 100 cm³, what is the cylinder's volume?
    1. A)100 cm³
    2. B)200 cm³
    3. C)300 cm³
    4. D)400 cm³
    Show answer

    Answer: 300 cm³

    Hint: A cone's volume is 1/3 of a cylinder with same dimensions.

  8. Q8.hard

    A sphere has volume \(\frac{256}{3}\pi\) cm³. Find the radius.
    1. A)3 cm
    2. B)4 cm
    3. C)5 cm
    4. D)6 cm
    Show answer

    Answer: 4 cm

    Hint: V = (4/3)πr³.

  9. Q9.hard

    A rectangular prism has a square base of side \(x\) and height \(2x\). If the volume is 128 cm³, find \(x\).
    1. A)2 cm
    2. B)3 cm
    3. C)4 cm
    4. D)5 cm
    Show answer

    Answer: 4 cm

    Hint: V = x² × 2x = 2x³.

These are 9 of the 60 questions available for Volume & Surface Area. Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.