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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 cube has side 8 cm. It is cut along diagonals of top face to get 4 equal parts. What is the total surface area (in cm2) of each part?

A) 96 + 64√2 B) 80 + 64√2
C) 96 + 48√2 D) 80 + 48√2
 
Answer & Explanation Answer: A) 96 + 64√2

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2 1895
Q:

PQRS is a square, M is the mid-point of PQ and N is a point on QR such that NR is two-third of QR. If the area of ΔMQN is 48 cm2 , then what is the length (in cm) of PR ?

A) 12√2 B) 12
C) 24 D) 24√2
 
Answer & Explanation Answer: D) 24√2

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1 1890
Q:

In a cyclic quadrilateral ABCD ∠BCD=120° and passes through the centre of the circle. Then ∠ABD = ?

A) 30° B) 40°
C) 50° D) 60°
 
Answer & Explanation Answer: A) 30°

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0 1863
Q:

The height of a cone is 45 cm. It is cut at a height of 15 cm from its base by a plane parallel to its base. If the volume of the smaller cone is 18480 cm3, then what is the volume (in cm3) of the original cone?

A) 34650 B) 61600
C) 36960 D) 62370
 
Answer & Explanation Answer: D) 62370

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1 1853
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 1846
Q:

Circum center of ΔABC is O. If ∡BAC = 75 and ∡BCA = 80 degrees,

 then what is the value of ∡OAC(in deg)?

A) 45 B) 65
C) 90 D) 95
 
Answer & Explanation Answer: B) 65

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0 1844
Q:

A solid cone of height 24 cm and radius of its base 8 cm is melted to form a solid cylinder of radius 6 cm and height 6 cm. In the whole process what
percent of material is wasted?

A) 48.5 B) 37.5
C) 57.8 D) 64
 
Answer & Explanation Answer: C) 57.8

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0 1835
Q:

An equilateral triangle ABC is inscribed in a circle of radius 20√3.
What is the length of the side of the triangle?

A) 30 cm B) 40 cm
C) 50 cm D) 60 cm
 
Answer & Explanation Answer: D) 60 cm

Explanation:
Radius of circumcircle of an equilateral triangle = side /√3
R = a/√3
a = R√3 = 20√3 *√3 = 60cm
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0 1828