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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:

D and E are points on side AB and AC of ΔABC. DE is parallel to BC. If AD:DB = 1:2 and area of ΔABC is 45 sq cm, what is the area (in sq cm) of quadrilateral BDEC?

A) 20 B) 40
C) 15 D) 30
 
Answer & Explanation Answer: B) 40

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0 1018
Q:

Find the curved surface area (in cm2) of a right circular cylinder of diameter 7 cm and height 6 cm.

A) 132 B) 110
C) 92 D) 154
 
Answer & Explanation Answer: A) 132

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0 1018
Q:

D and E are points on side AB and AC of ΔABC. DE is parallel to BC. If AD:DB = 2:3, what is the ratio of area of ΔADE and area of quadrilateral BDEC?

A) 4 : 21 B) 4 : 25
C) 4 : 29 D) 4 : 9
 
Answer & Explanation Answer: A) 4 : 21

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0 1016
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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1 1014
Q:

A tent is to be built in the form of a cylinder of radius 7 m surmounted by a cone of the same radius. If the height of the cylindrical part is 8 m and slant height of the conical part is 12 m, how much canvas will be required to build the tent? Allow 20% extra canvas for folding and stitching. (Take π = 22/7)

A) 1478.4 sq mts B) 2217.6 sq mts
C) 369.6 sq mts D) 739.2 sq mts
 
Answer & Explanation Answer: D) 739.2 sq mts

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0 1012
Q:

What is the sum of the measures of all the interior angles of a regular polygon of 5 sides?

A) 720 B) 1080
C) 1260 D) 540
 
Answer & Explanation Answer: D) 540

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0 1011
Q:

The base and hypotenuse of a right angled triangle is 12 cm and 5 cm respectively. Find the circum-radius (in cm) of the triangle.

 

A) 5 B) 6
C) 6.5 D) 7
 
Answer & Explanation Answer: C) 6.5

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1 1011
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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