Download the 3D Mensuration Volume and Surface Area MCQs with Free PDF for PPSC, FPSC, PMS, NTS, KPKPSC, and SPSC exam
3D mensuration is the branch of mathematics that deals with measuring three-dimensional objects. It is concerned with the calculation of the volume, surface area, and lateral surface area of objects such as cubes, cuboids, spheres, pyramids, and cones.
The volume of an object is the amount of space it occupies. The surface area is the total area of all the faces of an object. The lateral surface area is the area of all the sides of an object, excluding the top and bottom faces.
The formulas for calculating the volume, surface area, and lateral surface area of different 3D objects are as follows:
- Cube:
- Volume = side³
- Surface area = 6 × side²
- Cuboid:
- Volume = length × breadth × height
- Surface area = 2 × (length × breadth + breadth × height + length × height)
- Sphere:
- Volume = (4/3)πr³
- Surface area = 4πr²
- Pyramid:
- Volume = (1/3) × area of base × height
- Surface area = area of base + sum of lateral faces
- Cone:
- Volume = (1/3)πr²h
- Surface area = πrl + πr²
where:
- side is the length of one side of the cube
- length, breadth, and height are the dimensions of the cuboid
- r is the radius of the sphere
- area of base is the area of the base of the pyramid or cone
- l is the slant height of the cone
Here are some of the common formulas for calculating the volume, surface area, and lateral surface area of different 3D shapes:
- Cube: Volume = side³, Surface area = 6 × side²
- Cuboid: Volume = length × breadth × height, Surface area = 2(lb + bh + hl)
- Sphere: Volume = (4/3)πr³, Surface area = 4πr²
- Cone: Volume = (1/3)πr²h, Lateral surface area = πrl
- Pyramid: Volume = (1/3) × area of base × height, Lateral surface area = 1/2 × perimeter of base × slant height
To see more detail and more material visit www.superiorexam.pk .The MCQs are free to download, and they are a valuable resource for anyone who wants to learn more about competitive exam.
