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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:

The ratio of total surface area and volume of a sphere is 1 : 7. This sphere is melted to form small spheres of equal size. The radius of each small sphere is 1/6th the radius of the large sphere. What is the sum (in cm2) of curved surface areas of all small spheres?

A) 31276 B) 36194
C) 25182 D) 33264
 
Answer & Explanation Answer: D) 33264

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0 1131
Q:

A circle is inscribed in a square. If the length of the diagonal of the square is 14√2 cm, what is the area (in sq cm) of the circle?

A) 308 B) 462
C) 154 D) 616
 
Answer & Explanation Answer: C) 154

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Q:

The surface area of a sphere is 5544 cm2. Find its diameter (in cm).

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

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Q:

The base area of a right pyramid is 57 sq. units and height is 10 units. Then the volume of the pyramid is

A) 190 c. units B) 380 c. units
C) 540 c. units D) 570 c. units
 
Answer & Explanation Answer: A) 190 c. units

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0 1129
Q:

If the side of the equilateral triangle is 8√3 cm, then what is the length (in cm) of the in radius of the triangle?

A) 2 B) 4
C) 8√3 D) 16√3
 
Answer & Explanation Answer: B) 4

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0 1129
Q:

The total surface area of a cube is 337.5 cm². Find its side (in cm).

A) 8.5 B) 6.5
C) 5.5 D) 7.5
 
Answer & Explanation Answer: D) 7.5

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0 1129
Q:

An arc of 30° in one circle is double an arc in a second circle, the radius of which is three times the radius of the first. Then the angles subtended by the arc of the second circle at its centre is

A) 3° B) 4°
C) 5° D) 6°
 
Answer & Explanation Answer: C) 5°

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0 1126
Q:

T is a point on the common tangents at P of two circles and if TA and TB are resectively the other tangents at A and B to the two circles drawn from the point T then

A) TA = 2 TB B) TA = TB
C) TA = 1/2 TB D) 3TA = TB
 
Answer & Explanation Answer: B) TA = TB

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0 1125