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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 cylindrical vessel of radius 8 cm is partially filled with water. By how much will the water level rise if a sphere of radius 7 cm is completely immersed in this water?

A) 7.15 cm B) 14.3 cm
C) 21.45 cm D) 28.6 cm
 
Answer & Explanation Answer: A) 7.15 cm

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Q:

A square is inscribed in a circle. If the side of the square is 14 cm, what is the area (in sq.cm) of the circle?

A) 49π B) 77π
C) 121π D) 98π
 
Answer & Explanation Answer: D) 98π

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Q:

If the diameter of a circle is 35 cm, then what will be its circumference (in cm)?

A) 110 B) 220
C) 21 D) 42
 
Answer & Explanation Answer: A) 110

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0 1325
Q:

Thousand solid metallic spheres of diameter 6 cm are melted and recast into a new solid sphere. The diameter of the new sphere (in cm) is

A) 30 B) 90
C) 45 D) 60
 
Answer & Explanation Answer: D) 60

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0 1324
Q:

The surface area of a sphere is 5544 sq.cm. Find its diameter (in cm).

A) 42 B) 21
C) 84 D) 63
 
Answer & Explanation Answer: A) 42

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1 1323
Q:

Dodecahedron has 30 edges. How many vertices does it have?

A) 12 B) 16
C) 20 D) 10
 
Answer & Explanation Answer: C) 20

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2 1323
Q:

In ΔPQR, L and M are two points on the sides PQ and PR respectively such that LM II QR. If PL=2cm; LQ=6cm and PM=1.5 cm, then MR in cm is

A) 0.5 B) 4.5
C) 9 D) 8
 
Answer & Explanation Answer: B) 4.5

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0 1322
Q:

Two circles touch each other at point X. Two common tangents of the circles meet at point P and none of the tangents passes through X. These tangents touch the larger circle at points B and C. If the radius of the larger circle is 15 cm and CP = 20 cm, then what is the radius (in cm) of the smaller circle?

A) 3.5 B) 3.75
C) 4.25 D) 4.45
 
Answer & Explanation Answer: B) 3.75

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