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 Volume and Surface Area Questions

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FACTS  AND  FORMULAE  FOR  VOLUME  AND  SURFACE  AREA  QUESTIONS

 

 

I. CUBOID

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

1. Volume = (l x b x h)

2. Surface area = 2(lb +bh + lh) sq.units

3. Diagonal =l2+b2+h2 units

 

 

II. CUBE 

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

1. Volume = a3 cubic units.

2. Surface area = 6a2 sq.units

3. Diagonal = 3a units

 

 

III. CYLINDER 

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

1.Volume = πr2h cubic units 

2. Curved surface area = 2πrh sq.units

3. Total surface area = 2πrh+2πr2 sq.units

 

 

IV. CONE 

Let radius of base =r and Height = h. Then, 

1. Slant height, l=h2+r2 units

 

2. Volume = 13πr2h cubic units.

 

3. Curved surface area = πrlsq.units 

 

4. Total surface area = πrl+πr2sq.units

 

 

V. SPHERE 

Let the radius of the sphere be r. Then, 

1. Volume =43πr3 cubic units

2. Surface area = 4πr2 sq.units

 

 

VI. HEMISPHERE 

Let the radius of a hemisphere be r. Then, 

1. Volume = 23πr3 cubic units.

2. Curved surface area = 2πr2 sq.units

3. Total surface area = 3πr2 sq.units

 

Q:

ABCD is a quadrilateral with AB = 9 cm, BC = 40 cm, CD = 28 cm, DA = 15 cm and angle ABC is a right –angel
What is the area of quadrilateral ABCD?

A) 300 SQ.CM   B) 306 SQ.CM
C) 312 SQ.CM D) 316 SQ.CM
 
Answer & Explanation Answer: D) 316 SQ.CM

Explanation:
Area of quadrilateral ABCD = area of triangle ADC + area of triangle ABC
= 126 + ½ * 9 * 40 = 306
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Q:

Points P , Q and R are on a circle such that ∠PQR = 40° and ∠QRP = 60° . Then the subtended angle by arc QR at the centre is

A) 80° B) 120°
C) 140° D) 160°
 
Answer & Explanation Answer: D) 160°

Explanation:
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Q:

Three consecutive integers form the lengths of a right-angled triangle. How many sets of such three consecutive integers is/are possible?

A) Only one B) Only two
C) Only three D) Infinitely many
 
Answer & Explanation Answer: A) Only one

Explanation:

let n-1, n, n+1 be 3 consecutive integers

So

(n+1)^2= n^2+ (n-1)^2

(n+1)^2-(n-1)^2= n^2

4n = n^2

So n = 0 or n = 4

n can’t be 0 as n-1 will be negative then

So 3,4 and 5 is the only triplet formed.

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Q:

In triangle PQR, A is the point of intersection of all the altitudes and B is the point of intersection of all the angle bisectors of the triangle. If ∠PBR =105°, then what is the value of ∠PAR (in degrees)?

A) 60 B) 100
C) 105 D) 115
 
Answer & Explanation Answer: A) 60

Explanation:
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Q:

A solid cube is cut into 27 identical cubes. What is the percentage increase in the total surface area?

A) 150 B) 200
C) 300 D) 250
 
Answer & Explanation Answer: B) 200

Explanation:
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Q:

The line segment AB intersects the straight line CD at B; AB will be smallest when ∠ ABD (in degrees) is

A) 30 B) 60
C) 90 D) 45
 
Answer & Explanation Answer: C) 90

Explanation:
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Q:

The length of diagonal BD of a parallelogram ABCD is 36 cm. P and Q are the centroids of triangle ABC and triangle ADC respectively. What is the length (in cm) of PQ?

A) 6 B) 9
C) 12 D) 18
 
Answer & Explanation Answer: C) 12

Explanation:
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Q:

In triangle PQR, the sides PQ and PR are produced to A and B respectively. The bisectors of ∠AQR and ∠BRQ intersect at point O. If ∠QOR = 50°, then what is the value (in degrees) of ∠QPR?

A) 50 B) 60
C) 80 D) 100
 
Answer & Explanation Answer: C) 80

Explanation:
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