Take FREE!! Online Mettl Mock Test to Crack TechM and Other Companies Written Exams.
Get Off-Campus Placement Jobs Info !!!
TCS NQT Technical and Managerial Round Interview Questions

Quantitative Aptitude :: Volume and Surface Area

Volume and Surface Area Important Formulas


1. CUBOID:


A cuboid is a 3D shape. Cuboids have six faces, which form a convex polyhedron. Broadly, the faces of the cuboid can be any quadrilateral. More narrowly, cuboids are made from 6 rectangles, which are placed at right angles. A cuboid that uses all square faces is a cube.

Let length = l, breadth = b and height = h units. Then

\( \mathbb{i.} \) Volume = (l x b x h) cubic units.

\( \mathbb{ii.} \) Surface area = 2(lb + bh + lh) sq. units.

\( \mathbb{iii.} \) Diagonal = \(\sqrt{l^{2} \ + \ b^{2} \ + \ h^{2}}\) units.

2. CUBE:


In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex.

Let each edge of a cube be of length a. Then,

\( \mathbb{i.} \) Volume = a3 cubic units.

\( \mathbb{ii.} \) Surface area = 6a2 sq. units.

\( \mathbb{iii.} \) Diagonal = \(\sqrt{3}a\) units.

4. CONE:


A cone is a three-dimensional geometric shape that tapers smoothly from a flat base (frequently, though not necessarily, circular) to a point called the apex or vertex.

Let radius of base = r and Height (or length) = h. Then,

\( \mathbb{i.} \) Slant height \(l \ = \ \sqrt{h^{2} \ + \ r^{2}}\) units.

\( \mathbb{ii.} \) Volume = r\(\left( \frac{1}{3} \ pi r^{2}h \right)\) cubic units.

\( \mathbb{iii.} \) Curved surface area = \((\pi rl)\) sq. units.

\( \mathbb{iv.} \) Total surface area = \((\pi rl \ + \ \pi r^{2})\) sq. units.

4. CYLINDER:


A cylinder is one of the most basic curved geometric shapes, with the surface formed by the points at a fixed distance from a given line segment, known as the axis of the cylinder

Let radius of base = r and Height (or length) = h. Then,

\( \mathbb{i.} \) Volume = \(\left(\pi r^{2}h \right)\) cubic units.

\( \mathbb{ii.} \) Curved surface area = \(2(\pi rh)\) sq. units.

\( \mathbb{iii.} \) Total surface area = \(2\pi r(h \ + \ r)\) sq. units.

5. SPHERE:


Sphere, In geometry, the set of all points in three-dimensional space lying the same distance (the radius) from a given point (the centre), or the result of rotating a circle about one of its diameters.

Let the radius of the sphere be r. Then,

\( \mathbb{i.} \) Volume = \(\left( \frac{4}{3} \ pi r^{3} \right)\) cubic units.

\( \mathbb{ii.} \) surface area = \((4\pi r^{2})\) sq. units.

6. HEMISPHERE:


A hemisphere is the half of a sphere. When a sphere is cut into two halves, then the shape we get is called the hemisphere. A hemisphere has a curved surface and a flat base. The curved surface area of the hemisphere is half of the surface area of the sphere.

Let the radius of a hemisphere be r. Then,

\( \mathbb{i.} \) Volume = \(\left( \frac{2}{3} \ pi r^{3} \right)\) cubic units.

\( \mathbb{ii.} \) Curved surface area = \((2\pi r^{2})\) sq. units.

\( \mathbb{iv.} \) Total surface area = \((3\pi r^{2})\) sq. units.

Note: 1 litre = 1000 cm3.