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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:

Which of the following option is CORRECT about the figure shown below?

A) OA – AR = OB + BR B) OA + AR = OB – BR
C) OA + AR = OB + BR D) None of these
 
Answer & Explanation Answer: C) OA + AR = OB + BR

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Q:

The tangents drawn at points A and B of a circle with centre O, meet at P. If ∠AOB = 120° and AP = 6 cm, then what is the area of triangle (in cm2) APB?

A) 6√3 B) 8√3
C) 9 D) 9√3
 
Answer & Explanation Answer: D) 9√3

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Q:

An angle is smaller than its supplementary by 30°. What is the measure of the angle?

A) 75° B) 105°
C) 60° D) 30°
 
Answer & Explanation Answer: A) 75°

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Q:

Two circles touch each other at point X. Two common tangents of the circles meet at point P and none of the tangents passes through X. These tangents touch the larger circle at points B and C. If the radius of the larger circle is 15 cm and CP = 20 cm, then what is the radius (in cm) of the smaller circle?

A) 3.5 B) 3.75
C) 4.25 D) 4.45
 
Answer & Explanation Answer: B) 3.75

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Q:

PQR is an equilateral triangle. MN is drawn parallel to QR such that M is on PQ and N is on PR. If PN = 6 cm, then the length of MN is

A) 3 cm B) 6 cm
C) 12 cm D) 4.5 cm
 
Answer & Explanation Answer: B) 6 cm

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Q:

What is the value of Cot 60°- Cos 45°?

A) (9 - 2√3)/9 B) (2√6 - 1)/√3
C) (1 - 2√3)/2 D) (√2 - √3)/√6
 
Answer & Explanation Answer: D) (√2 - √3)/√6

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Q:

Find the total surface area (in cm²) of a right circular cone of diameter 14 cm and slant height 10 cm.

 

A) 374 B) 570
C) 428 D) 524
 
Answer & Explanation Answer: A) 374

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Q:

The radius of a sphere and right circular cylinder is 'r'. Their volumes are equal. The ratio of the height and radius of the cylinder is:

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

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