Volume Formulas

A table of volume formulas and surface area formulas used to calculate the volume and surface area of three-dimensional geometrical shapes: cube, cuboid, prism, solid cylinder, hollow cylinder, cone, pyramid, sphere and hemisphere.

Shape	Volume Formula	Surface Area Formula
Cube	s3 where s = length of the side	6s2 where s = length of the side
Cuboid	lwh where l = length, w = width, h = height	2(lw + lh + wh)  where l = length, w = width, h = height
Prism	area of base × height	2 × area of base + perimeter of base × height
Cylinder	πr2h where r = radius, h = height	2πr (r + h) where r = radius, h = height
Hollow Cylinder	πh(R2 − r2) where R = radius of the outer surface, r = radius of the inner surface	2πrh + 2πRh + 2(πR2 − πr2) where R = radius of the outer surface, r = radius of the inner surface
Cone	1/3 πr2h  where r = radius, h = height	πr (r + s) where r = radius, s = slant height
Pyramid	1/3 × area of base ×  height	Any pyramid = area of base + area of each of the lateral faces Regular pyramid = area of base + ½  ps where p = perimeter of the base, s = slant height Square pyramid = b2 + 2bs where b = length of the base, s = slant height
Sphere	4/3 πr3 where r = radius	4πr2 where r = radius
Hemisphere	2/3 πr3 where r = radius	3πr3 where r = radius

Data Sufficiency

Directions to Solve:

In each of the questions below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and Give answer


(A) If the data in statement I alone are sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question
(B) If the data in statement II alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question
(C) If the data either in statement I alone or in statement II alone are sufficient to answer the question
(D) If the data given in both statements I and II together are not sufficient to answer the question and
(E) If the data in both statements I and II together are necessary to answer the question.


1.Question: In which year was Rahul born ?

Statements:

Rahul at present is 25 years younger to his mother.
Rahul's brother, who was born in 1964, is 35 years younger to his mother.

A.I alone is sufficient while II alone is notsufficient
B.II alone is sufficient while I alone is not sufficient
C.Either I or II is sufficient
D.Neither I nor II is sufficient
E.Both I and II are sufficient

Answer & Explanation

Answer: Option E

Explanation:

From both I and II, we find that Rahul is (35 - 25) = 10 years older than his brother, who was born in 1964. So, Rahul was born in 1954.

2.Question: What will be the total weight of 10 poles, each of the same weight ?

Statements:

One-fourth of the weight of each pole is 5 kg.
The total weight of three poles is 20 kilograms more than the total weight of two poles.

A.I alone is sufficient while II alone is not sufficient
B.II alone is sufficient while I alone is not sufficient
C.Either I or II is sufficient
D.Neither I nor II is sufficient
E.Both I and II are sufficient

Answer & Explanation

Answer: Option C

Explanation:

From I, we conclude that weight of each pole = (4x5) kg = 20 kg.
So, total weight of 10 poles = (20 x 10) kg = 200 kg.
From II, we conclude that:
Weight of each pole = (weight of 3 poles) - (weight of 2 poles) = 20 kg.
So, total weight of 10 poles = (20 x 10) kg = 200 kg.

3.Question: How many children does M have ?

Statements:

H is the only daughter of X who is wife of M.
K and J are brothers of M.

A.I alone is sufficient while II alone is not sufficient
B.II alone is sufficient while I alone is not sufficient
C.Either I or II is sufficient
D.Neither I nor II is sufficient
E.Both I and II are sufficient

Answer & Explanation

Answer: Option D

Explanation:
From I, we conclude that H is the only daughter of M. But this does not indicate that M has no son. The information given in II is immaterial.

4.Question: How much was the total sale of the company ?

Statements:

The company sold 8000 units of product A each costing Rs. 25.
This company has no other product line.

A.I alone is sufficient while II alone is not sufficient
B.II alone is sufficient while I alone is not sufficient
C.Either I or II is sufficient
D.Neither I nor II is sufficient
E.Both I and II are sufficient

Answer & Explanation

Answer: Option E

Explanation:

From I, total sale of product A = Rs. (8000 x 25) = Rs. 200000.

From II, we know that the company deals only in product A.
This implies that sale of product A is the total sale of the company, which is Rs. 200000.

5.Question: The last Sunday of March, 2006 fell on which date ?

Statements:

The first Sunday of that month fell on 5th.
The last day of that month was Friday.

A.I alone is sufficient while II alone is not sufficient
B.II alone is sufficient while I alone is not sufficient
C.Either I or II is sufficient
D.Neither I nor II is sufficient
E.Both I and II are sufficient

Answer & Explanation

Answer: Option C

Explanation:

From I, we conclude that 5th, 12th, 19th and 26th of March, 2006 were Sundays.
So, the last Sunday fell on 26th.
From II, we conclude that 31st March, 2006 was Friday. Thus, 26th March, 2006 was the last Sunday of the month.