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 Volume and Surface Area Questions

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 = (πrl)sq.units 

 

4. Total surface area = (πrl+πr2)sq.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:

Find the curved surface area (in cm2) of a right circular cylinder of diameter 14 cm and height 8 cm.

 

A) 308 B) 352
C) 327 D) 371
 
Answer & Explanation Answer: B) 352

Explanation:
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0 14757
Q:

In the figure AMB = 130°, then what is the value (in deg) of ABQ?

 

A) 40 B) 50
C) 60 D) 90
 
Answer & Explanation Answer: B) 50

Explanation:
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3 14738
Q:

Two cones have their heights in the ratio 1:3 and the radii of their bases in the ratio 3:1. Find the ratio of their volumes.

A) 3:1 B) 2:1
C) 4:1 D) 5:1
 
Answer & Explanation Answer: A) 3:1

Explanation:

v1v2=r12Hr22H

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28 14569
Q:

The cost of the paint is rs.36.50 per kg. if 1kg of paint covers 16sq.ft, how much will it cost to paint outside of a cube having 8 feet each side

A) Rs.962 B) Rs.672
C) Rs.546 D) Rs.876
 
Answer & Explanation Answer: D) Rs.876

Explanation:

surface area of a cube= 6 x (8 x 8) = 384 sq.ft  

quantity of paint required=(384/16)=24kg  

cost of painting= 36.5 x 24 = Rs.876

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12 14558
Q:

∆DEF is right angled at E. If m∠F = 45°, then find the value of (tanD - √3/2).

 

A) -√3/2 B) -1/2√3
C) (2-√3)/2 D) (3√3-1)/3
 
Answer & Explanation Answer: C) (2-√3)/2

Explanation:
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0 14548
Q:

Find the total surface area (in cm2) of a right circular cylinder of diameter 7 cm and height 6 cm.

 

A) 187   B) 209  
C) 163   D) 149
 
Answer & Explanation Answer: B) 209  

Explanation:
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0 14523
Q:

The slant height of a right circular cone is 10 m and its height is 8 m. Find the area of its curved surface

A) 40pi sq.m B) 50pi sq.m
C) 60pi sq.m D) 70pi sq.m
 
Answer & Explanation Answer: C) 60pi sq.m

Explanation:

ke

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22 14328
Q:

Find the volume (in cub.cm) of a hemisphere of diameter 28 cm.

 

A) 4789.67   B) 3675  
C) 2732 D) 5749.33
 
Answer & Explanation Answer: D) 5749.33

Explanation:
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1 14264