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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 solid sphere of diameter 7 cm is cut into two equal halves. What will be the increase (in cm2) in the total surface area ?

A) 77 B) 154
C) 87 D) 38.5
 
Answer & Explanation Answer: A) 77

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1 1019
Q:

In the figure, a circle touches quadrilateral ABCD. If AB = 2x + 3, BC = 3x - 1, CD = x + 6 and DA = x + 4, then what is the value of x?

A) 3 B) 4.5
C) 6 D) 6.5
 
Answer & Explanation Answer: C) 6

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1 1017
Q:

A right circular cylinder is formed. A = sum of total surface area and the area of the two bases. B = the curved surface area of this cylinder. If A : B = 3 : 2 and the volume of cylinder is 4312 cm3, then what is the sum of area (in cm2) of the two bases of this cylinder?

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

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0 1013
Q:

In an isosceles ΔABC, AD is the median to the unequal side meeting BC at D. DP is the angle disector of ∠ADB and PQ is drawn parallel to BC meeting AC at Q. Then the measure of ∠PDQ is

A) 130° B) 90°
C) 180° D) 45°
 
Answer & Explanation Answer: B) 90°

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0 994
Q:

Due to increase of k% in the side, the area of a square increases by 69%. What is the value of k?

A) 30 B) 33
C) 34.5 D) 35
 
Answer & Explanation Answer: A) 30

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0 993
Q:

An equilateral triangle ABC is inscribed in a circle of radius 20√3.
The centroid of the triangle ABC is at a distance d from the vertex A. What is d equal to ?

A) 15 cm B) 20 cm
C) 20√3 cm D) 30√3 cm
 
Answer & Explanation Answer: C) 20√3 cm

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0 990
Q:

Sum of lengths of all edges of a cube is 84 cm, find its volume?

A) 686 cubic cms B) 343 cubic cms
C) 171.5 cubic cms D) 514.5 cubic cms
 
Answer & Explanation Answer: B) 343 cubic cms

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0 984
Q:

In a ∆ABC, BC is extended upto D, ∡ACD =120°, ∡B = 1/2 A. Then ∡A is

A) 60° B) 75°
C) 80° D) 90°
 
Answer & Explanation Answer: C) 80°

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0 980