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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:

If the sum of the interior angles of a regular polygon is 1260 deg , then how many sides does it have?

A) 10 B) 12
C) 15 D) 9
 
Answer & Explanation Answer: D) 9

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Q:

The external and the internal radii of a hollow right circular cylinder of height 15 cm are 6.75 cm and 5.25 cm respectively. If it is melted to form a solid cylinder of height half of the orignal cylinder, then the radius of the solid cylinder is

A) 6 cm B) 7.25 cm
C) 6.5 cm D) 7 cm
 
Answer & Explanation Answer: A) 6 cm

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Q:

If the measure of the exterior angle of a regular polygon is 72 deg then how many sides does it have?
 

A) 6 B) 8
C) 9 D) 5
 
Answer & Explanation Answer: D) 5

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Q:

Two regular polygons are such that the ratio between their number of sides is 1:2 and the ratio of measures of their interior angles is 3:4. Then the number of sides of each polygon are

A) 10, 20 B) 4, 8
C) 3, 6 D) 5, 10
 
Answer & Explanation Answer: D) 5, 10

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Q:

Calculate the length of the tangent (in cm) which is drawn from a point at a distance of 13 cm from the centre and the largest chord of that circle is 10 cm.

A) 10 B) 12
C) 15 D) 16
 
Answer & Explanation Answer: B) 12

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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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Q:

The line passing through (4,3) and (y,0) is parallel to the line passing through (­-1,-­2) and (3,0). Find y?

A) -1 B) -2
C) 2 D) -5
 
Answer & Explanation Answer: B) -2

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Q:

The sum of the lengths of the edges of a cube is equal to four times the perimeter of a square. If a quarter of the numerical value of the volume of the cube is equal to the numerical value of the area of the square, then the length of one side of the square is

A) 27/16 units B) 10.5 units
C) 9/4 units D) 27 units
 
Answer & Explanation Answer: A) 27/16 units

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