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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:

PQ is the chord of a circle whose centre is O. ROS is a line segment originating from a point R on the circle that intersect PQ produced at point S such that QS = OR. If ∠QSR = 30°, then what is the value (in degrees)of POR?

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

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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:

If the angles of a triangle are in the ratio of 2 : 5 : 8, then find the value of the smallest angle.

A) 36 deg B) 18 deg
C) 12 deg D) 24 deg
 
Answer & Explanation Answer: D) 24 deg

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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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Q:

In a triangle, one of the angles is three times the smallest and another is two times the smallest angle. Calculate the smallest angle.

 

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

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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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0 735
Q:

___ is the point at which the perpendicular bisectors of the sides meet and the center of the circle that circumscribes the triangle is ____.

A) Incenter, Circumcenter B) Circumcenter, Circumcenter
C) Circumcenter, Incenter D) Orthocenter, Circumcenter
 
Answer & Explanation Answer: B) Circumcenter, Circumcenter

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1 720
Q:

The perimeter and the length of one of the diagonals of a rhombus is 26 cm and 5 cm respectively. Find the length of its other diagonal (in cm).

 

A) 6 B) 12
C) 24 D) 18
 
Answer & Explanation Answer: B) 12

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