(Part IX) – common aptitude for competitive exam like IBPS consists of shortcut methods, tips and tricks to solve question from Partnerships, Surds and Indices and Pipes and Cistern. This particular learning section** (Part X)** includes another two very important sections from *quantitative aptitudes including “Volume and Surface Area”, “Races and Games”*.

Shortcut methods and tricks to solve questions from **‘Volume and Surface Area’** are given below:

Volume and Surface formula for solids, sphere, prism, cuboid:

**Cuboid Formula:**

Let’s consider the length of the cuboid is p units, breadth is a units and height is s units. Then,

a. Volume = (p x a x s) cubic units

b. Surface Area = 2 (pa + as + ps) square units

c. Diagonal = √(p^{2} + a^{2} + s^{2}) units

——————————————————————————————————————-

**Cube Formula:**

If each edge of a cube is considered to be of length x, then

a. Volume = x^{3} cubic units

b. Surface Area = 6x^{2 }square units

c. Diagonal = √3x units.

——————————————————————————————————————-

**Cylinder Formula:**

Let the radius of base = I, height or length = m. Then,

a. Volume = ∏l2m cubic units

b. Curved Surface Area = 2∏lm square units.

c. Total Surface Area = 2∏l (l + m)

——————————————————————————————————————-

**Cone Formula:**

Let the radius of base = l and height or length = m. Then,

a. Slant height S = √(l^{2 }+ m^{2}) units

b. Volume = 1/3 (∏l^{2}m) cubic units

c. Curved Surface Area = ∏lm square units

d. Total Surface Area = (∏lm + ∏l^{2}) square units

——————————————————————————————————————-

**Sphere Formula:**

If the radius of the sphere r, Then

a. Volume = 4/3 (∏r^{3}) cubic units

b. Surface Area = (4∏r^{2}) square units

——————————————————————————————————————-

Shortcut methods and tricks to solve questions from **‘Races and Games’** are given below:

**Races:** A race is a contest of speed in running, riding, driving, sailing, rowing etc over a particular distance.

**Race Course: ** It’s defined as the ground or path on which contests are conducted.

**Starting Point: **It’s a particular point from which the actual race starts

**Winning Point (or Goal): **It’s a particular point where a face is finished.

**Dead Heat Race:** If all the persons contesting the race reach the winning point (goal) exactly at the same time, then that particular race is called Dead Heat Race.

**Winner: **When a person reaches the winning post first, then he is declared as winner.

Suppose P and Q are two contestants in a race. Then considering the below mathematical interpretations:

**P beats Q by t seconds** – P finishes the race t seconds before Q

**P gives a start of t seconds to Q** – P starts t seconds after Q starts from the same starting point.

**P gives Q a start of S metres** – While P starts from the starting point, Q starts s meters ahead from the same starting point at the same time. To cover a race of 50 metres in this case, A will have to cover 50 metres while B will have to cover only (50 – s) metres.

In a game of 60, P can give Q 40 points – While P scores 60 points, Q scores only 60-40=20 points.

If X is n times as fast as Y and X gives Y a start of s meters, then the length of the race course, so that X and Y reaches the winning post at the same time =** s [n / (n-1)]** metres.

If X can run s metre race in t_{1}** **seconds and Y in t_{2}** _{ }**seconds, where t

_{1}< t

_{2}

**,**then X beats Y by a distance:

**(s / t**

_{2}) (t_{2}– t_{1}**)**metre

**(……to be continued in Part XI)**

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