Important Mensuration Questions

Mensuration means measuring shapes like squares, circles, and triangles. In this article, we’ll help you understand Mensuration questions and provide simple answers. Whether you’re a student getting ready for tests or just want to get better at math, you’ll find easy explanations and step-by-step solutions.

In this article, we’ll cover important topics like finding the size of areas, volumes, and more. Let’s explore Mensuration together to make math easier for you!

Mensuration Questions with Solutions

Question 1: Find the area of a rectangle with a length of 8 units and a width of 5 units.

Solution:

Area = Length × Width
Area = 8 units × 5 units
Area = 40 square units.

Question 2: Calculate the perimeter of a square with a side length of 6 units.

Solution:

Perimeter = 4 × Side Length
Perimeter = 4 × 6 units
Perimeter = 24 units.

Question 3: Determine the volume of a cube with an edge length of 4 units.

Solution:

Volume = Edge Length³
Volume = 4 units³
Volume = 64 cubic units.

Question 4: Find the circumference of a circle with a radius of 5 units. (Use π ≈ 3.14)

Solution:

Circumference = 2 × π × Radius
Circumference = 2 × 3.14 × 5 units
Circumference ≈ 31.4 units.

Question 5: Calculate the area of a triangle with a base of 10 units and a height of 8 units.

Solution:

Area = (Base × Height) / 2
Area = (10 units × 8 units) / 2
Area = 40 square units.

Question 6: Determine the perimeter of a rectangle with a length of 12 units and a width of 7 units.

Solution:

Perimeter = 2 × (Length + Width)
Perimeter = 2 × (12 units + 7 units)
Perimeter = 2 × 19 units
Perimeter = 38 units.

Question 7: Find the volume of a rectangular prism with dimensions: length = 6 units, width = 4 units, and height = 5 units.

Solution:

Volume = Length × Width × Height
Volume = 6 units × 4 units × 5 units
Volume = 120 cubic units.

Question 8: Calculate the circumference of a circle with a radius of 8 units. (Use π ≈ 3.14)

Solution:

Circumference = 2 × π × Radius
Circumference = 2 × 3.14 × 8 units
Circumference ≈ 50.24 units.

Question 9: Find the area of a triangle with a base of 15 units and a height of 9 units.

Solution:

Area = (Base × Height) / 2
Area = (15 units × 9 units) / 2
Area = 67.5 square units.

Question 10: Determine the volume of a cube with an edge length of 7 units.

Solution:

Volume = Edge Length³
Volume = 7 units³
Volume = 343 cubic units.

Question 11: Find the surface area of a rectangular prism with dimensions: length = 10 units, width = 6 units, and height = 8 units.

Solution:

Surface Area = 2 × (Length × Width + Width × Height + Height × Length)
Surface Area = 2 × (10 units × 6 units + 6 units × 8 units + 8 units × 10 units)
Surface Area = 2 × (60 + 48 + 80) square units
Surface Area = 376 square units.

Question 12: Calculate the volume of a cone with a radius of 5 units and a height of 12 units. (Use π ≈ 3.14)

Solution:

Volume = (1/3) × π × Radius² × Height
Volume = (1/3) × 3.14 × (5 units)² × 12 units
Volume ≈ 314.16 cubic units.

Question 13: Determine the total surface area of a cylinder with a radius of 6 units and a height of 10 units. (Use π ≈ 3.14)

Solution:

Total Surface Area = 2 × π × Radius² + 2 × π × Radius × Height
Total Surface Area = 2 × 3.14 × (6 units)² + 2 × 3.14 × 6 units × 10 units
Total Surface Area ≈ 452.16 square units.

Question 14: Find the volume of a sphere with a radius of 9 units. (Use π ≈ 3.14)

Solution:

Volume = (4/3) × π × Radius³
Volume = (4/3) × 3.14 × (9 units)³
Volume ≈ 3053.04 cubic units.

Question 15: Calculate the lateral surface area of a cone with a slant height of 13 units and a radius of 5 units. (Use π ≈ 3.14)

Solution:

Lateral Surface Area = π × Radius × Slant Height
Lateral Surface Area = 3.14 × 5 units × 13 units
Lateral Surface Area ≈ 204.5 square units.

Question 16: Determine the volume of a frustum of a cone with radii of the top and bottom bases as 8 units and 12 units, respectively, and a height of 15 units. (Use π ≈ 3.14)

Solution:

Volume = (1/3) × π × Height × (Top Radius² + Bottom Radius² + Top Radius × Bottom Radius)
Volume = (1/3) × 3.14 × 15 units × (8 units² + 12 units² + 8 units × 12 units)
Volume ≈ 4987.2 cubic units.

Question 17: Find the surface area of a torus (doughnut shape) with a major radius of 10 units and a minor radius of 3 units. (Use π ≈ 3.14)

Solution:

Surface Area = 4 × π × Major Radius × Minor Radius
Surface Area = 4 × 3.14 × 10 units × 3 units
Surface Area ≈ 376.8 square units.

Question 18: Calculate the volume of a hemisphere with a radius of 14 units. (Use π ≈ 3.14)

Solution:

Volume = (2/3) × π × Radius³
Volume = (2/3) × 3.14 × (14 units)³
Volume ≈ 12323.36 cubic units.

Question 19: Determine the volume of a frustum of a cone with radii of the top and bottom bases as 8 units and 12 units, respectively, and a height of 15 units. (Use π ≈ 3.14)

Solution:

Volume = (1/3)πh(R² + r² + Rr)
Volume = (1/3) * 3.14 * 15 * (12² + 8² + 12 * 8)
Volume = (1/3) * 3.14 * 15 * (144 + 64 + 96)
Volume = (1/3) * 3.14 * 15 * 304
Volume ≈ 4,541.2 cubic units

Question 20: Find the lateral surface area of a cone with a slant height of 10 units and a radius of 6 units. (Use π ≈ 3.14)

Solution:

Lateral Surface Area = πrl
Lateral Surface Area = 3.14 * 6 * 10
Lateral Surface Area ≈ 188.4 square units

Question 21: Calculate the volume of a hemisphere with a radius of 9 units. (Use π ≈ 3.14)

Solution:

Volume = (2/3)πr³
Volume = (2/3) * 3.14 * 9³
Volume = (2/3) * 3.14 * 729
Volume ≈ 1,526.04 cubic units

Question 22: Find the total surface area of a cylinder with a radius of 5 units and a height of 12 units. (Use π ≈ 3.14)

Solution:

Total Surface Area = 2πr(r + h)
Total Surface Area = 2 * 3.14 * 5 * (5 + 12)
Total Surface Area ≈ 565.2 square units

Question 23: Determine the volume of a cube with a surface area of 150 square units. (Assume all sides are equal)

Solution:

Volume = (1/6) * Surface Area^3/2
Volume = (1/6) * 150^3/2
Volume = (1/6) * 150 * √150
Volume = (1/6) * 150 * 12.25
Volume ≈ 305.42 cubic units

Question 24: Determine the volume of a sphere inscribed inside a cube. The cube has a surface area of 486 square units. (Use π ≈ 3.14)

Solution:

Given the surface area of the cube, we can calculate the length of each side of the cube.
Surface Area of Cube = 6s² = 4866s² = 486s² = 486 / 6s² = 81s = √81s = 9 units
Now, we can calculate the volume of the inscribed sphere using the cube’s side length as the sphere’s diameter.
Diameter of Sphere (d) = 9 units
Radius of Sphere (r) = d / 2 = 9 / 2 = 4.5 units
Volume of Sphere = (4/3)πr³Volume of Sphere = (4/3) * 3.14 * (4.5³)Volume of Sphere ≈ 381.69 cubic units

Question 25: Find the surface area of a regular tetrahedron with each side measuring 6 units. (Use √3 ≈ 1.732)

Solution:

A regular tetrahedron has 4 equilateral triangular faces. To find its surface area, we need to calculate the area of one of these triangles and then multiply it by 4.
Area of Equilateral Triangle = (sqrt(3)/4) * a²
Area of One Triangle = (1.732/4) * 6²
Area of One Triangle ≈ 15.588 square units
Now, multiply the area of one triangle by 4 to find the surface area of the tetrahedron.
Surface Area of Tetrahedron = 4 * 15.588
Surface Area of Tetrahedron ≈ 62.352 square units

Conclusion

Mensuration may sound complex, but with the right guidance and practice, it becomes much simpler. We’ve covered a variety of Mensuration questions and provided clear solutions to help you grasp these mathematical concepts. Whether you’re calculating the area of your room or the volume of a box, understanding Mensuration is essential in our daily lives.

Remember, practice makes perfect, so keep working on these problems to improve your skills. With patience and determination, you can conquer Mensuration and build a strong foundation in mathematics. We hope this article has been a valuable resource in your journey to mathematical proficiency. Keep exploring, keep learning, and keep solving those Mensuration problems with confidence!