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:

The circumference of a circle is equal to the perimeter of an equilateral Δ. If the radius of the circle is 14 cm what is the length of the side of the equilateral Δ?

A) 88 cm B) 88/3 cm
C) 88/√3 cm D) 88√3 cm
 
Answer & Explanation Answer: B) 88/3 cm

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Q:

In triangle ABC, ∠ABC = 90°. BP is drawn perpendicular to AC. If ∠BAP = 30°, then what is the value (in degrees) of ∠PBC?

A) 30 B) 36
C) 45 D) 60
 
Answer & Explanation Answer: A) 30

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Q:

Δ ABC is right angled at B. If m∠A = 30°, what is the length of AB (in cm), if AC = 10 cm?

A) 5 B) 5√3
C) 10√3 D) 10
 
Answer & Explanation Answer: B) 5√3

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Q:

The length of the radius of a circle with centre O is 5 cm and the length of the chord AB is 8 cm. The distance of the chord AB from the point O is

A) 2 cm B) 3 cm
C) 4 cm D) 15 cm
 
Answer & Explanation Answer: B) 3 cm

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Q:

Find the sum of interior angles of a decagon?

A) 1620° B) 2520°
C) 1800° D) 1440°
 
Answer & Explanation Answer: D) 1440°

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Q:

O is the centre of the circle and ∠AOB = 150°, and the shaded portion is x part of the circular region, then x = ?

A) 1/12 B) 1/9
C) 1/6 D) 1/4
 
Answer & Explanation Answer: C) 1/6

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Q:

 In ΔDEF measure of angle E is 90 deg. If tanD = 4/3, and DE = 6cm, then what is the length (in cm) of side EF?

A) 10 B) 5
C) 8 D) 4
 
Answer & Explanation Answer: C) 8

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Q:

Δ PQR is right angled at Q. If m∠R = 60°, what is the length of PR (in cm), if RQ = 4√3 cm?

A) 8 B) 4
C) 8/√3 D) 8√3
 
Answer & Explanation Answer: D) 8√3

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