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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:

In the given figure, ABC is a right angled triangle. ABC = 90 deg and ACB = 60 deg. If the radius of the smaller circle is 2 cm, then what is the radius (in cm) of the larger circle?

A) 4 B) 6
C) 4.5 D) 7.5
 
Answer & Explanation Answer: B) 6

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0 1411
Q:

O is the circumcentre of ΔABC. If AO = 8 cm, then the length of BO is

A) 12 cm B) 3 cm
C) 6 cm D) 8 cm
 
Answer & Explanation Answer: D) 8 cm

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0 1403
Q:

If the curved surface area of a right circular cone is 3080 sq cm and its slant height is 35 cm, find its total surface area?

A) 11088 sq cm B) 1848 sq cm
C) 5544 sq cm D) 2772 sq cm
 
Answer & Explanation Answer: C) 5544 sq cm

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1 1396
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 1393
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 1373
Q:

In the given figure, PQRS is a square of side 20 cm and SR is extended to point T. If the length of QTis 25 cm, then what is the distance (in cm) between the centers O1 and O2 of the two circles?

A) 5√10 B) 4√10
C) 8√5 D) 16√2
 
Answer & Explanation Answer: A) 5√10

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1 1370
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 1365
Q:

G is the centroid of ΔABC. If AG = BC, then measure of ∠BGC is

A) 45° B) 60°
C) 90° D) 120°
 
Answer & Explanation Answer: C) 90°

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0 1356