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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 tent is to be built in the form of a cylinder of radius 7 m surmounted by a cone of the same radius. If the height of the cylindrical part is 8 m and slant height of the conical part is 12 m, how much canvas will be required to build the tent? Allow 20% extra canvas for folding and stitching. (Take π = 22/7)

A) 1478.4 sq mts B) 2217.6 sq mts
C) 369.6 sq mts D) 739.2 sq mts
 
Answer & Explanation Answer: D) 739.2 sq mts

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0 816
Q:

The area of the base of a cone is 64pi sq.cm while its slant height is 17 cm. This cone is remolded to obtain a solid sphere. The radius of this sphere will be

 

A) 2303 cm B) 2403 cm
C) 8303 cm D) 6.5 cm
 
Answer & Explanation Answer: A) 2303 cm

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1 810
Q:

The minimum number of straight lines required to construct the given figure is ___.

A) 11 B) 12
C) 9 D) 10
 
Answer & Explanation Answer: A) 11

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1 809
Q:

 The line bisecting all the three angles of a triangle meets at a common point. This point is known as ______________.

A) circum-center B) centroid
C) orthocenter D) in-center
 
Answer & Explanation Answer: D) in-center

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0 807
Q:

Possible measures of three angles of a triangle are

A) 33°, 42°, 115° B) 40°, 70°, 80°
C) 30°, 60°, 100° D) 50°, 60°, 70°
 
Answer & Explanation Answer: D) 50°, 60°, 70°

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0 806
Q:

Find the total surface area (in cm²) of a right circular cylinder of diameter 28 cm and height 12 cm.

 

A) 2200   B) 2080
C) 1920 D) 2288
 
Answer & Explanation Answer: D) 2288

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1 803
Q:

Consider the following figure shown below and choose which of the following equation is correct about the similarity of both triangles?

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

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0 793
Q:

If DE is parallel to BC and bisects the other two sides of the triangle ABC such that the ratio AD/DB = 5/13 and the length of the part EC is 26 cm. Then determine the length of AE (in cm).

A) 5 B) 10
C) 15 D) 20
 
Answer & Explanation Answer: B) 10

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0 786