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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:

The radius of a hemisphere is 14 cm, find its volume?

A) 11498.66 cubic cm B) 1916.44 cubic cm
C) 2874.67 cubic cm D) 5749.33 cubic cm
 
Answer & Explanation Answer: D) 5749.33 cubic cm

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Q:

The triangle ABC and DEF are similar to each other. The measure of the angle A and E is 67 and 83 degree respectively. What is the value of angle C?

A) 20°   B) 30°
C) 40° D) 50°
 
Answer & Explanation Answer: B) 30°

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Q:

A chord of a circle is equal to its radius. A tangent is drawn to the circle at an extremity of the chord. The angle between the tangent and the chord is

A) 30° B) 45°
C) 60° D) 75°
 
Answer & Explanation Answer: A) 30°

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Q:

ΔABC is right angled at B. BD is its altitude. AD = 4 cm and DC = 12 cm. What is the value of AB (in cm)?

A) 9 B) 10
C) 6 D) 8
 
Answer & Explanation Answer: D) 8

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Q:

In ΔABC, the medians AD and BE meet at G. The ratio of the areas of ΔBDG and the quadrilateral GDCE is

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

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Q:

Points P , Q and R are on a circle such that ∠PQR = 40° and ∠QRP = 60° . Then the subtended angle by arc QR at the centre is

A) 80° B) 120°
C) 140° D) 160°
 
Answer & Explanation Answer: D) 160°

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Q:

A tent is to be built in the form of a cylinder of radius 5 m surmounted by a cone of the same radius. If the height of the cylindrical part is 6 m and slant height of the conical part is 10 m, how much canvas will be required to build the tent? Allow 20% extra canvas for folding and stitching. (Take π = 22/7)

A) 829.72 sq mts B) 414.86 sq mts
C) 1244.58 sq mts D) 207.43 sq mts
 
Answer & Explanation Answer: B) 414.86 sq mts

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Q:

Incentre of Δ ABC is I. ∠ABC = 90° and ∠ACB = 70°. ∠AIC is

A) 115° B) 100°
C) 110° D) 105°
 
Answer & Explanation Answer: C) 110°

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