# 20+ Volume and Surface Area Questions and Answers | Quantitative Aptitude

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:

1. 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.

1. 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.

1. 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.

Cylinders and Cones:

1. 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.

1. 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.

1. 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:

1. 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.

1. 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.

1. 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:

1. 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.

1. 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.

1. 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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