Understanding volume and surface area questions is crucial for understanding and solving various problems and concepts you might come across during your exams like **UPSC CSE**, **NDA**, **CDS**, **banking exams** ( **SBI PO**, **RBI Assistant**, **IBPS RRB**) and Management Exams like the **CAT Exam**. Whether you’re a school student preparing for competitive exams or simply someone curious about the world around you, mastering these fundamental ideas is essential.

This article serves as your one-stop guide, with 20+ volume and surface area questions along with detailed solutions and explanations, including step-by-step instructions. By diving into these examples, you’ll gain the knowledge and confidence to conquer any challenge related to these key geometric concepts.

## Formula of Surface Area and Volume

Before we go to Volume and Surface Area Questions the questions, let’s have a look at the important formulas:

Volume:

- Cuboid: l × b × h
- Cube: a^3
- Cylinder: πr^2h
- Cone: (1/3)πr^2h
- Sphere: (4/3)πr^3
- Pyramid: (1/3) × base area × height

Surface Area:

- Cuboid: 2(lb + bh + hl)
- Cube: 6a^2
- Cylinder: 2πr^2 + 2πrh (lateral + base)
- Cone: πr^2 + πrl (lateral + base)
- Sphere: 4πr^2

## Practise these Volume and Surface Area Questions

Now, buckle up and prepare to master volume and surface area questions with these 20+ questions and answers:

**Cuboids and Cubes:**

- Find the volume of a cuboid with length 10 cm, breadth 5 cm, and height 8 cm.

Solution:

- Step 1: Identify the relevant formula: Volume of a cuboid = l × b × h
- Step 2: Substitute the given values: Volume = 10 cm × 5 cm × 8 cm
- Step 3: Calculate the result: Volume = 400 cm^3

Therefore, the volume of the cuboid is 400 cm^3.

- Calculate the surface area of a cube with side length 7 cm.

Solution:

- Step 1: Identify the relevant formula: Surface area of a cube = 6a^2
- Step 2: Substitute the given value: Surface area = 6 × 7 cm^2
- Step 3: Calculate the result: Surface area = 294 cm^2

Therefore, the surface area of the cube is 294 cm^2.

- A cuboid has a volume of 240 cm^3 and a base area of 40 cm^2. Find its height.

Solution:

- Step 1: Identify the relevant formula: Volume = l × b × h
- Step 2: Rearrange the formula to solve for height: h = Volume / Base area
- Step 3: Substitute the given values: h = 240 cm^3 / 40 cm^2
- Step 4: Calculate the result: h = 6 cm

Therefore, the height of the cuboid is 6 cm.

**Also Read: ****Questions of Syllogism Reasoning | Verbal Reasoning**

**Cylinders and Cones:**

- Determine the volume of a cylinder with radius 4 cm and height 12 cm.

Solution:

- Step 1: Identify the relevant formula: Volume of a cylinder = πr^2h
- Step 2: Substitute the given values: Volume = π × (4 cm)^2 × 12 cm
- Step 3: Calculate the result: Volume = 192π cm^3

Therefore, the volume of the cylinder is 192π cm^3.

- Calculate the lateral surface area of a cone with radius 5 cm and slant height 13 cm.

Solution:

- Step 1: Identify the relevant formula: Lateral surface area of a cone = πrl
- Step 2: Substitute the given values: Lateral surface area = π × 5 cm × 13 cm
- Step 3: Calculate the result: Lateral surface area = 65π cm^2

Therefore, the lateral surface area of the cone is 65π cm^2.

- A cylindrical water tank has a diameter of 100 cm and a height of 150 cm. How much water can it hold?

Solution:

- Step 1: Convert diameter to radius: radius = diameter / 2 = 100 cm / 2 = 50 cm
- Step 2: Identify the

**Spheres:**

- Find the volume of a sphere with radius 6 cm.

Solution:

- Step 1: Identify the relevant formula: Volume of a sphere = (4/3)πr^3
- Step 2: Substitute the given value: Volume = (4/3)π × (6 cm)^3
- Step 3: Calculate the result: Volume = 288π cm^3

Therefore, the volume of the sphere is 288π cm^3.

- Calculate the surface area of a sphere with radius 5 cm.

Solution:

- Step 1: Identify the relevant formula: Surface area of a sphere = 4πr^2
- Step 2: Substitute the given value: Surface area = 4π × (5 cm)^2
- Step 3: Calculate the result: Surface area = 100π cm^2

Therefore, the surface area of the sphere is 100π cm^2.

- A spherical balloon has a surface area of 144π cm^2. Find its radius.

Solution:

- Step 1: Identify the relevant formula: Surface area of a sphere = 4πr^2
- Step 2: Rearrange the formula to solve for radius: r^2 = Surface area / 4π
- Step 3: Substitute the given value: r^2 = 144π cm^2 / 4π
- Step 4: Calculate the radius: r = √(36 cm^2) = 6 cm

Therefore, the radius of the spherical balloon is 6 cm.

**Mixed Questions:**

- A rectangular box has a length of 15 cm, breadth of 10 cm, and height of 8 cm. What is the total surface area?

Solution:

- Step 1: Identify the relevant formula: Total surface area of a cuboid = 2(lb + bh + hl)
- Step 2: Substitute the given values: Total surface area = 2(15 cm × 10 cm + 10 cm × 8 cm + 15 cm × 8 cm)
- Step 3: Calculate the result: Total surface area = 680 cm^2

Therefore, the total surface area of the rectangular box is 680 cm^2.

- A right circular cone has a diameter of 16 cm and a height of 12 cm. Find its volume and lateral surface area.

Solution:

- Step 1: Convert diameter to radius: radius = diameter / 2 = 16 cm / 2 = 8 cm
- Step 2: Identify the relevant formulas:
- Volume of a cone = (1/3)πr^2h
- Lateral surface area of a cone = πrl

- Step 3: Substitute the given values:
- Volume = (1/3)π × (8 cm)^2 × 12 cm
- Lateral surface area = π × 8 cm × 13 cm (where slant height is calculated using the Pythagorean theorem)

- Step 4: Calculate the results:
- Volume = 64π cm^3
- Lateral surface area = 104π cm^2

Therefore, the volume of the cone is 64π cm^3 and the lateral surface area is 104π cm^2.

- A cylindrical vessel has a radius of 7 cm and a height of 14 cm. It is filled with water up to a height of 10 cm. Calculate the volume of water in the vessel.

Solution:

- Step 1: Identify the relevant formula: Volume of a cylinder = πr^2h
- Step 2: Calculate the volume of the cylinder: Volume = π × (7 cm)^2 × 14 cm = 308π cm^3
- Step 3: Calculate the volume of the empty space above the water: Volume = π × (7 cm)^2 × 4 cm = 196π cm^3
- Step 4: Calculate the volume of water by subtracting the empty space from the total volume: Volume of water = 308π cm^3 – 196π cm^3 = 112π cm^3

Therefore, the volume of water in the vessel is 112π cm^3.

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