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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 = (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:

Three circle C1, C2 and C3 with radii r1, r2 and r3 (where r1<r2<r3) are placed as shown in the given figure. What is the value of r2?

A) √( r1r3) B) ( r1 + r3)/2
C) (2 r1r2)/( r1 + r2) D) √( r1 + r3)
 
Answer & Explanation Answer: A) √( r1r3)

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Q:

In the given figure, ∡QRU = 72°, ∡TRS = 15°, ∡PSR = 95° , then what is the value (in deg) of ∡PQR?

A) 85 B) 95
C) 75 D) 90
 
Answer & Explanation Answer: B) 95

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0 2141
Q:

Which measurement unit represents volume?

A) milliliter B) Cubic centimeter
C) Meter cube D) All of the above
 
Answer & Explanation Answer: D) All of the above

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9 2055
Q:

In the given figure, MNOP is a square of side 6 cm. What is the value ( in cm ) of radius of circle?

A) 4.25 B) 3.75
C) 3.5 D) 4.55
 
Answer & Explanation Answer: B) 3.75

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0 1959
Q:

Radius of base of a hollow cone is 8 cm and its height is 15 cm. A sphere of largest radius is put inside the cone. What is the ratio of radius of base of cone to the radius of sphere?

A) 5 : 3 B) 4 : 1
C) 2 : 1 D) 7 : 3
 
Answer & Explanation Answer: A) 5 : 3

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6 1948
Q:

A regular triangular pyramid is cut by 2 planes which are parallel to its base. The planes trisects the altitude of the pyramid. Volume of top, middle and bottom part is V1, V2 and V3 respectively. What is the value of V1 :V2 : V3?

A) 1 : 8 : 27 B) 1 : 8 : 19
C) 2 : 9 : 27 D) 1 : 7 : 19
 
Answer & Explanation Answer: D) 1 : 7 : 19

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0 1939
Q:

The base of a pyramid is a rectangle whose length and breadth are 16 cm and 12 cm respectively. If the length of all the lateral edges passing through the vertex of the right rectangular pyramid is 26 cm, then find the volume of the pyramid in cubic centimeter?

A) 1536 B) 1024
C) 718 D) 2072
 
Answer & Explanation Answer: A) 1536

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10 1855
Q:

A sphere of radius 21 cm is cut into 8 identical parts by 3 cuts (1 cut along each axis). What will be the total surface area (in cm2) of each part?

A) 844.5 B) 1732.5
C) 1039.5 D) 1115.6
 
Answer & Explanation Answer: B) 1732.5

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3 1831