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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:

A wooden bowl is in shape of a hollow hemisphere of internal radius 7 cm and thickness 1 cm. What is the total surface area (in sq.cm) of the bowl? (Take:  = 22/7)

A) 710.29 B) 757.43
C) 355.14 D) 908.91
 
Answer & Explanation Answer: B) 757.43

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0 1296
Q:

Curved surface area of a cylinder is 528 sq cm. If circumference of its base is 44 cm, find the height of the cylinder?

A) 12 cm B) 24 cm
C) 36 cm D) 6 cm
 
Answer & Explanation Answer: A) 12 cm

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1 1294
Q:

O is the orthocentre of∆ABC, and if ∠BOC = 110° then ∠BAC will be

A) 110° B) 70°
C) 100° D) 90°
 
Answer & Explanation Answer: B) 70°

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0 1285
Q:

The sum of length, breadth and height of a cuboid is 22 cm and the length of its diagonal is 14 cm.
What is the surface area of the cuboid?

A) 288 sq.cm B) 216 sq.cm
C) 144 sq.cm D) Cannot be determined due to insufficient data
 
Answer & Explanation Answer: A) 288 sq.cm

Explanation:
Let lengths, breadth and height of cuboid be l, b and h respectively
According to question
l+b+h = 22cm......(i)
and
√(l^2+b^2+h^2) = 14cm .....(ii)
Surface area of cuboid = 2(lb+bh+lh)
Squaring eq (i) gives
l2+b2+h2+ 2(lb+bh+lh) = 484
Substituting l^2+b^2+h^2 from eq (i)
2(lb+bh+lh) = 484 -196 = 288 sq.cm
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0 1279
Q:

In an isosceles ΔABC, AD is the median to the unequal side meeting BC at D. DP is the angle disector of ∠ADB and PQ is drawn parallel to BC meeting AC at Q. Then the measure of ∠PDQ is

A) 130° B) 90°
C) 180° D) 45°
 
Answer & Explanation Answer: B) 90°

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0 1277
Q:

Considering two opposite vertices of a square of side ‘a’ as centres, two circular arcs are drawn within the square joining the other two vertices, thus forming two sectors. What is the common area in these two sectors?

A) a2π+12 B) a
C) a2π2-1 D) πa/2
 
Answer & Explanation Answer: C) a2π2-1

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4 1269
Q:

PQRS is a square whose side is 16 cm. What is the value of the side (in cm) of the largest regular octagon that can be cut from the given square?

A) 8 – 4√2 B) 16 + 8√2
C) 16√2 – √16 D) 16 – 8√2
 
Answer & Explanation Answer: C) 16√2 – √16

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0 1265
Q:

In ΔDEF, G and H are points on side DE and DF respectively. GH is parallel to EF. If G divides DE in the ratio 1:3 and HF is 7.2 cm, find length of DF?

A) 2.4 cm B) 4.8 cm
C) 3.6 cm D) 9.6 cm
 
Answer & Explanation Answer: D) 9.6 cm

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