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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 1573
Q:

In a triangle PQR, S and T are the points on PQ and PR respectively, such that ST II QR and PS/SQ=3/5,PR =6cm, then PT is

A) 2 cm B) 2.25 cm
C) 3.5 cm D) 4 cm
 
Answer & Explanation Answer: B) 2.25 cm

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0 1571
Q:

In a quadrilateral PQRS, l_S= 90°. A circle (o, r) touches the sides PQ, QR, RS and SP at A, B, C and D respectively. If QR= 38 cm, RS = 25 cm and QA = 27 cm, find 'r'.

A) 16 cm B) 12 cm
C) 14 cm D) 10 cm
 
Answer & Explanation Answer: C) 14 cm

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1 1569
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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0 1568
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 1567
Q:

A solid has 12 vertices and 30 edges. How many faces does it have?

A) 22 B) 24
C) 26 D) 20
 
Answer & Explanation Answer: D) 20

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1 1558
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 1555
Q:

In ∆ABC two medians BE and CF intersects at the point O and P,Q are the midpoints of BO and CO respectively. If the length of PQ=3cm, then the length of FE will be

A) 3 cm B) 6 cm
C) 9 cm D) 12 cm
 
Answer & Explanation Answer: A) 3 cm

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0 1555