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 Volume and Surface Area Questions

Popular Latest Rated Important Formulae

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:

What will be the sum of the measures all the interior angles of a polygon having 14 sides?

A) 2520° B) 2160°
C) 2880° D) 3240°
 
Answer & Explanation Answer: B) 2160°

Explanation:
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0 1133
Q:

In ΔPQR, S and T are points on side PQ and PR respectively. ST is parallel to QR. If lengths of PS, SQ and PR are 6 cm, 9 cm and 12.5 cm respectively, what is the length of TR?

A) 7.5 cm B) 5 cm
C) 10 cm D) 2.5 cm
 
Answer & Explanation Answer: A) 7.5 cm

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1 1130
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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0 1128
Q:

10 identical solid spherical balls of radius 3 cm are melted to form a single sphere. In this process 20% of solid is wasted. What is the radius (in cm) of the bigger sphere?

A) 24 B) 12
C) 8 D) 6
 
Answer & Explanation Answer: D) 6

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0 1127
Q:

The diameters of two cylinders are in the ratio 3:2 and their volumes are equal. The ratio of their heights is

A) 2:3 B) 3:2
C) 9:4 D) 4:9
 
Answer & Explanation Answer: D) 4:9

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2 1122
Q:

Three solid spheres have their radii r1, r2 and r3. The spheres are melted to form a solid sphere of bigger radius. Then the radius of the new sphere is

A) r1+r2+r3 B) r12+r22+r3212
C) r13+r23+r3313 D) r14+r24+r3414
 
Answer & Explanation Answer: C) r13+r23+r3313

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0 1117
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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1 1115
Q:

If the lengths of two parallel chords in a circle of radius 10 cm are 12 cm and 16 cm, then what is the distance between these two chords?

A) 1 cm or 7 cm B) 2 cm or 14 cm
C) 3 cm or 21 cm D) 4 cm or 28 cm
 
Answer & Explanation Answer: B) 2 cm or 14 cm

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1 1111