Volume and Surface Area Questions

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:

Find the volume (in cub.cm) of a hemisphere of diameter 21 cm.

A) 2235.5 B) 2425.5
C) 2040 D) 1860
 
Answer & Explanation Answer: B) 2425.5

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Q:

In triangle ABC, BAC = 90 deg and AD is perpendicular to BC. If AD = 6cm and BD = 4cm, then the length of BC is

A) 10 cm B) 12 cm
C) 13 cm D) 15 cm
 
Answer & Explanation Answer: C) 13 cm

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Q:

In triangle ABC measure of angle B is 90 deg. If sinA = 24/25, and AB = 1.4cm, then what is the length (in cm) of side BC.

A) 4.8 B) 5
C) 3 D) 5.6
 
Answer & Explanation Answer: A) 4.8

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Q:

The radius of a hemisphere is 21 cm, what is its volume? (Take π = 22/7)

A) 38808 cubic cms B) 9702 cubic cms
C) 19404 cubic cms D) 29106 cubic cms
 
Answer & Explanation Answer: C) 19404 cubic cms

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Q:

In a triangle the length of the side opposite the angle which measures 30° is 9 cm, what is the length of the side opposite to the angle which measures 60°?

A) 3√3 cm B) 3/2 cm
C) 9/2 cm D) 9√3 cm
 
Answer & Explanation Answer: D) 9√3 cm

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Q:

The height of a cone is 24 cm and the area of the base is 154 cm2 . What is the curved surface area (in cm2) of the cone?

A) 484 B) 550
C) 525 D) 515
 
Answer & Explanation Answer: B) 550

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Q:

ABC is a right angled triangle with angle A = 90 deg. Then the value of cos2A+cos2B+cos2C is

A) 2 B) 1
C) 0 D) 3
 
Answer & Explanation Answer: B) 1

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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 = 2:5 and area of ΔADE is 8 sq cm, what is the ratio of area of ΔADE: area of quadrilateral BDEC?

A) (4:45) B) (45:4)
C) (8:45) D) (45:8)
 
Answer & Explanation Answer: A) (4:45)

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