About Surface Area & Volume — Class 9 ICSE

Find surface area and volume of cylinders, cones, spheres, and hemispheres. This topic is part of the ICSE Class 9 mathematics syllabus (chapter: Chapter 18). 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.

What you'll learn in Surface Area & Volume

• Introduction to Surface Area & Volume
• Cylinders: Surface Area and Volume
• Cones: Surface Area and Volume
• Spheres and Hemispheres: Surface Area and Volume
• Composite Solids and Exam Preparation

Interactive lesson · about 15 minutes · checkpoint question after every unit

Surface Area & Volume — solved examples for Class 9 ICSE

Practice questions on Surface Area & Volume

1. Q1.easy

   For calculating the curved surface area of a cone, why is the slant height (l) used instead of the perpendicular height (h)?

   1. A)The slant height is always larger than the perpendicular height, giving a more accurate area.
   2. B)The curved surface of a cone is formed by a sector of a circle, and its radius corresponds to the cone's slant height.
   3. C)Perpendicular height is only used for calculating the volume of a cone.
   4. D)Slant height simplifies the calculations by avoiding square roots.
   Show answer

   Answer: The curved surface of a cone is formed by a sector of a circle, and its radius corresponds to the cone's slant height.

   Hint: Imagine unrolling the curved surface of a cone into a flat 2D shape. What shape would it be, and how would its dimensions relate to the cone?

2. Q2.easy

   A student is asked to find the total surface area of a solid hemisphere. They correctly calculate its curved surface area as 2πr². What additional surface area must they include to find the total surface area?

   1. A)πr²
   2. B)2πr²
   3. C)3πr²
   4. D)4πr²
   Show answer

   Answer: πr²

   Hint: Remember that a solid hemisphere is half of a sphere, but it also has a flat base.

3. Q3.easy

   Ravi calculated the volume of a cylinder with radius 'r' and height 'h' as 2πr(r+h). Which of the following statements correctly identifies Ravi's mistake?

   1. A)Ravi used the formula for Curved Surface Area instead of Volume.
   2. B)Ravi used the formula for Total Surface Area of a cylinder instead of Volume.
   3. C)Ravi used the formula for the circumference of the base multiplied by height.
   4. D)Ravi used the formula for the surface area of a sphere.
   Show answer

   Answer: Ravi used the formula for Total Surface Area of a cylinder instead of Volume.

   Hint: Recall the standard formulas for the volume, curved surface area, and total surface area of a cylinder.

4. Q4.medium

   Find the total surface area of a cone whose radius is 7 cm and height is 24 cm. (Use π = 22/7)

   1. A)550 cm²
   2. B)628 cm²
   3. C)704 cm²
   4. D)792 cm²
   Show answer

   Answer: 704 cm²

   Hint: First, calculate the slant height (l) using the radius (r) and height (h) with the Pythagorean theorem. Then use the formula for Total Surface Area.

5. Q5.medium

   Calculate the surface area of a sphere with a diameter of 14 cm. (Use π = 22/7)

   1. A)154 cm²
   2. B)308 cm²
   3. C)462 cm²
   4. D)616 cm²
   Show answer

   Answer: 616 cm²

   Hint: Remember that the diameter is twice the radius. The surface area formula for a sphere depends on its radius.

6. Q6.medium

   What is the volume of a hemispherical bowl with a radius of 3.5 cm? (Use π = 22/7)

   1. A)44.92 cm³
   2. B)89.83 cm³
   3. C)179.67 cm³
   4. D)224.58 cm³
   Show answer

   Answer: 89.83 cm³

   Hint: The volume of a hemisphere is half the volume of a full sphere.

7. Q7.hard

   A right circular cone is inscribed in a hemisphere such that its base is on the flat surface (base) of the hemisphere and its vertex touches the spherical part. If the radius of the hemisphere is 7 cm, what is the volume of the cone?

   1. A)(736/3) cm³
   2. B)(1078/3) cm³
   3. C)(1372/3) cm³
   4. D)(1715/3) cm³
   Show answer

   Answer: (1078/3) cm³

   Hint: Visualize the setup. When a cone is inscribed this way, its radius and height are directly related to the hemisphere's radius.

8. Q8.hard

   Consider two solids: a sphere and a hemisphere. If both have the same volume, what is the ratio of the surface area of the sphere to the total surface area of the hemisphere?

   1. A)(2 / ∛2)
   2. B)(4 / (3 × ∛4))
   3. C)(3 / (2 × ∛2))
   4. D)(5 / (3 × ∛2))
   Show answer

   Answer: (4 / (3 × ∛4))

   Hint: First, establish the relationship between the radii of the sphere and the hemisphere using their equal volumes. Then, express their surface areas in terms of a single radius and find the ratio.

9. Q9.hard

   A solid toy is in the form of a hemisphere surmounted by a right circular cone. The height of the cone is 2 cm and the diameter of the base is 4 cm. If a right circular cylinder circumscribes the toy, find the difference between the total surface area of the cylinder and the total surface area of the toy. (Use π = 3.14)

   1. A)4π(2 - √2) cm²
   2. B)4π(4 - √2) cm²
   3. C)8π(2 - √2) cm²
   4. D)8π(4 - √2) cm²
   Show answer

   Answer: 4π(4 - √2) cm²

   Hint: First, determine the dimensions of the circumscribing cylinder. Remember that the total surface area of the toy includes the curved surface area of the cone and the curved surface area of the hemisphere, as its base is internal.

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