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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:

ABCD is a quadrilateral with AB = 9 cm, BC = 40 cm, CD = 28 cm, DA = 15 cm and angle ABC is a right –angel
What is the area of quadrilateral ABCD?

A) 300 SQ.CM   B) 306 SQ.CM
C) 312 SQ.CM D) 316 SQ.CM
 
Answer & Explanation Answer: D) 316 SQ.CM

Explanation:
Area of quadrilateral ABCD = area of triangle ADC + area of triangle ABC
= 126 + ½ * 9 * 40 = 306
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1 1620
Q:

ΔXYZ is similar to ΔPQR. If ratio of Perimeter of ΔXYZ and Perimeter of ΔPQR is 4:9 and if PQ = 27 cm, then what is the length of XY (in cm)?

A) 9 B) 12
C) 16 D) 15
 
Answer & Explanation Answer: B) 12

Explanation:
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1 1618
Q:

Point P (8 , 5) is the midpoint of segment AB. Co-ordinates of A are (5, y) and B are (x, -3). What is the value of x?

A) -11 B) 11
C) 7 D) -7
 
Answer & Explanation Answer: B) 11

Explanation:
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1 1616
Q:

The diameters of two cylinders are in the ratio 3:2 and their volumes are equal. The ratio of their heights is

A) 2:3 B) 3:2
C) 9:4 D) 4:9
 
Answer & Explanation Answer: D) 4:9

Explanation:
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2 1615
Q:

What will be the sum of the measures all the interior angles of a polygon having 14 sides?

A) 2520° B) 2160°
C) 2880° D) 3240°
 
Answer & Explanation Answer: B) 2160°

Explanation:
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0 1614
Q:

An equilateral triangle ABC is inscribed in a circle of radius 20√3.
The centroid of the triangle ABC is at a distance d from the vertex A. What is d equal to ?

A) 15 cm B) 20 cm
C) 20√3 cm D) 30√3 cm
 
Answer & Explanation Answer: C) 20√3 cm

Explanation:
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0 1609
Q:

In triangle PQR, the sides PQ and PR are produced to A and B respectively. The bisectors of ∠AQR and ∠BRQ intersect at point O. If ∠QOR = 50°, then what is the value (in degrees) of ∠QPR?

A) 50 B) 60
C) 80 D) 100
 
Answer & Explanation Answer: C) 80

Explanation:
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0 1605
Q:

In the given figure, the length of arc BC of the given circle is 44 cm. If O is the centre of circle, then what is the radius (in cm) of the circle?

A) 7 B) 14
C) 28 D) 35
 
Answer & Explanation Answer: C) 28

Explanation:
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