Class 9 Math of Space: Surface Area and Volume Mock Test (CBSE)

Topics in Math of Space: Surface Area and Volume

• Surface area and volume of cuboids and cubes
• Surface area and volume of a right circular cylinder
• Surface area and volume of a right circular cone
• Pyramids
• Surface area and volume of a sphere
• Hemispheres
• Guesstimates: estimating areas and volumes around us

Math of Space: Surface Area and Volume practice questions with answers

1. Q1Multiple choice·1 mark
   If the radius of a sphere is doubled, its surface area becomes how many times the original surface area?

   1. (a)8 times
   2. (b)4 times
   3. (c)16 times
   4. (d)2 times
   Show answer and step marks

   1. Correct option: (b) $4$ times+1

   Answer: (b)
2. Q2Multiple choice·1 mark
   The radius of the base of a right circular cylinder is $7\text{ cm}$ and its height is $10\text{ cm}$. What is the curved surface area of the cylinder? (Use $\pi = \frac{22}{7}$)

   1. (a)$440\text{ cm}^2$
   2. (b)$880\text{ cm}^2$
   3. (c)$1540\text{ cm}^2$
   4. (d)$220\text{ cm}^2$
   Show answer and step marks

   1. Correct option: (a) $440\text{ cm}^2$. Curved surface area of a cylinder = $2\pi rh = 2 \times \frac{22}{7} \times 7 \times 10 = 440\text{ cm}^2$.+1

   Answer: (a)
3. Q3Multiple choice·1 mark
   The total surface area of a solid hemisphere of radius $r$ is given by:

   1. (a)$3\pi r^2$
   2. (b)$6\pi r^2$
   3. (c)$2\pi r^2$
   4. (d)$4\pi r^2$
   Show answer and step marks

   1. Correct option: (a) $3\pi r^2$+1

   Answer: (a)
4. Q4Multiple choice·1 mark
   Which of the following is the most reasonable guesstimate for the volume of a standard classroom?

   1. (a)$20\text{ m}^3$
   2. (b)$2000\text{ m}^3$
   3. (c)$200\text{ m}^3$
   4. (d)$20,000\text{ m}^3$
   Show answer and step marks

   1. Correct option: (c) $200\text{ m}^3$+1

   Answer: (c)
5. Q5Assertion and reason·1 mark
   Assertion (A): If the edge of a cube is increased to 3 times its original length, its volume becomes 27 times. Reason (R): The volume of a cube of edge $a$ is given by $V = a^3$.

   1. (a)Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
   2. (b)Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
   3. (c)Assertion (A) is true but Reason (R) is false.
   4. (d)Assertion (A) is false but Reason (R) is true.
   Show answer and step marks

   1. Correct option: (a)+1

   Answer: (a)
6. Q6Short answer·3 marks
   A glass paperweight is shaped like a right pyramid with a square base of side 6 cm and vertical height 4 cm. The apex lies vertically above the centre of the square base. (a) Find the volume of the paperweight. [1] (b) Find the slant height of the pyramid, that is, the distance from the apex to the midpoint of a base edge. [1] (c) Find the lateral surface area of the pyramid, excluding the square base. [1]
   Show answer and step marks

   1. (a) Volume = (1/3) × base area × height = (1/3) × 6 × 6 × 4 = 48 cm³.+1
   2. (b) Half the base edge is 3 cm, so slant height = √(4² + 3²) = √25 = 5 cm.+1
   3. (c) Lateral area = 4 × (1/2) × 6 × 5 = 60 cm².+1

   Answer: (a) 48 cm³; (b) 5 cm; (c) 60 cm²

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