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:

In an isosceles trapezium ______.

A) Opposite sides are parallel B) Opposite angles are supplementary
C) Opposite angles are not equal D) Diagonals bisect opposite angles
 
Answer & Explanation Answer: B) Opposite angles are supplementary

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Q:

Three angles of a quadrilateral are 60°,90°and 100°. Then the fourth angle of the quadrilateral is

A) 95° B) 100°
C) 110° D) 115°
 
Answer & Explanation Answer: C) 110°

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Q:

The diameter of a circle is equal to the side of the square. What is the area of the square if the area of the circle is 49π sq cm?

A) 196 sq cm B) 154 sq cm
C) 124 sq cm D) 98 sq cm
 
Answer & Explanation Answer: A) 196 sq cm

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Q:

A chord of length 60 cm is at a distance of 16 cm from the centre of a circle. What is the radius (in cm) of the circle?

A) 17 B) 34
C) 51 D) 68
 
Answer & Explanation Answer: B) 34

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0 909
Q:

In ΔPQR, PQ = PR = 18 cm, AB and AC are parallel to lines PR and PQ respectively. If A is the mid-point of QR, then what is the perimeter (in cm) of quadrilateral ABPC?

A) 18 B) 28
C) 32 D) 36
 
Answer & Explanation Answer: D) 36

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Q:

The height and the total surface area of a right circular cylinder are 4 cm and 8π sq.cm. respectively. The radius of the base of cylinder is

A) (2√2 - 2) cm B) (2 - √2) cm
C) 2 cm D) √2 cm
 
Answer & Explanation Answer: A) (2√2 - 2) cm

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Q:

One internal angle of a rhombus of side 12 cm is 120°. What is the length of its longer diagonal?

A) 6√3 cm B) 12√2 cm
C) 6√2 cm D) 12√3 cm
 
Answer & Explanation Answer: D) 12√3 cm

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Q:

In ΔPQR, ∠QPR = 45° and the bisectors of ∠PQR and ∠PRQ meets at O. What is the value (in degrees) of ∠QOR?

A) 107.5 B) 112.5
C) 117.5 D) 122.5
 
Answer & Explanation Answer: B) 112.5

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