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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:

­ A wooden bowl is in shape of a hollow hemisphere of internal radius 8 cm and thickness 1 cm. Find the total surface area of the bowl?

A) 964.85 sq cms B) 1125.14 sq cms
C) 1687.71 sq cms D) 281.29 sq cms
 
Answer & Explanation Answer: A) 964.85 sq cms

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Q:

In triangle ABC, a line is drawn from the vertex A to a point D on BC. If BC = 9 cm and DC = 3 cm, then what is the ratio of the areas of triangle ABD and triangle ADC respectively?

A) 1 : 1 B) 2 : 1
C) 3 : 1 D) 4 : 1
 
Answer & Explanation Answer: B) 2 : 1

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Q:

The base of a prism is in the shape of an equilateral triangle. If the perimeter of the base is 18 cm and the height of the prism is 20 cm, then what is the volume (in cm3) of the prism?

A) 60√3 B) 30√6
C) 60√2 D) not know
 
Answer & Explanation Answer: D) not know

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Q:

In a triangle ABC, AD is angle bisector of ∠A and AB : AC = 3 : 4. If the area of triangle ABC is 350 cm2, then what is the area (in cm2) of triangle ABD?

A) 150 B) 200
C) 210 D) 240
 
Answer & Explanation Answer: A) 150

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Q:

Length of the sides of a triangle are a, b, c respectively. If a2 + b2 + c2 = ab +bc + ca then the triangle is

A) isosceles B) equilateral
C) scalene D) right­-angled
 
Answer & Explanation Answer: B) equilateral

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Q:

A regular hexagonal base prism has height 8 cm and side of base is 4 cm. What is the total surface area (in cm2) of the prism?

A) 54(3 + √3) B) 36(3 + √3)
C) 48(4 + √3) D) 24(4 + √3)
 
Answer & Explanation Answer: C) 48(4 + √3)

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Q:

Find the curved surface area (in cm2) of a right circular cylinder of diameter 28 cm and height 12 cm.

A) 968 B) 924
C) 856 D) 1056
 
Answer & Explanation Answer: D) 1056

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Q:

Which of the set of three sides can't form a triangle?

A) 5 cm, 6 cm, 7 cm B) 5 cm, 8 cm, 15 cm
C) 8 cm, 15 cm, 18 cm D) 6 cm, 7 cm, 11 cm
 
Answer & Explanation Answer: B) 5 cm, 8 cm, 15 cm

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