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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 volume of a right circular cone, with a base radius the same as its altitude, and the volume of a hemisphere are equal. The ratio of the radii of the cone to the hemisphere is

A) 2 : 1 B) √2 : 1
C) 23 : 1 D) 33 : 23
 
Answer & Explanation Answer: C) 23 : 1

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Q:

What is the sum of the measures of all the interior angles of a regular polygon of 6 sides?

A) 1080 B) 1260
C) 1440 D) 720
 
Answer & Explanation Answer: D) 720

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Q:

The length of the diagonal and the breadth of a rectangle are 29 cm and 20 cm respectively. Find its perimeter (in cm).

 

A) 164 B) 82
C) 21 D) 42
 
Answer & Explanation Answer: B) 82

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0 397
Q:

A shuttle cock used for playing badminton has the shape of a frustum of a cone mounted on a hemisphere. The external diameters of the frustum are 5cm and 2cm, the height of the entire shuttle cock is 7cm. Find the external surface area.

A) 80 sq.cm B) 73.38 sq.cm
C) 74.29 sq.cm D) 74.30 sq.cm
 
Answer & Explanation Answer: A) 80 sq.cm

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Q:

The area of the base of a cone is 64pi sq.cm while its slant height is 17 cm. This cone is remolded to obtain a solid sphere. The radius of this sphere will be

 

A) 2303 cm B) 2403 cm
C) 8303 cm D) 6.5 cm
 
Answer & Explanation Answer: A) 2303 cm

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Q:

In a right angled triangle, the hypotenuse is 4 cm longer than the perpendicular which is 4 cm longer than the base. Calculate the length of hypotenuse.

A) 12 Cm B) 10 Cm
C) 20 Cm D) 15 Cm
 
Answer & Explanation Answer: C) 20 Cm

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Q:

The number of diagonals in a pentadecagon is

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

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Q:

Choose the correct option for the following figure.

A) AB=BD B) AC=CD
C) BC=AB D) AD
 
Answer & Explanation Answer: B) AC=CD

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