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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:

If the volume of a cylinder is 385 cubic cm and height is 10 cm, find its radius?

A) 7 cm B) 10.5 cm
C) 3.5 cm D) 1.75 cm
 
Answer & Explanation Answer: C) 3.5 cm

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Q:

Curved surface area of a cylinder is 660 sq cm. If circumference of its base is 44 cm, find the volume of the cylinder?

A) 4620 cubic cm B) 2310 cubic cm
C) 6930 cubic cm D) 1155 cubic cm
 
Answer & Explanation Answer: B) 2310 cubic cm

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Q:

The area of a triangle ABC is 63 sq.units. Two parallel lines DE, FG, are drawn such that they divide the line segments AB and AC into three equal parts. What is the area of the quadrilateral DEGF?

 

 

A) 28 sq.units B) 35 sq.units
C) 21 sq.units D) 48 sq.units
 
Answer & Explanation Answer: C) 21 sq.units

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Q:

The point of intersection of all the angle bisector of a triangle is ______ of the triangle.

A) Incenter B) Circumcenter
C) Centroid D) Orthocenter
 
Answer & Explanation Answer: A) Incenter

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Q:

Two adjacent sides of a parallelogram are 21 cms and 20 cms. The diagonal joining the end points of these two sides is 29 cms. The area of the parallelogram (in sq.cms) is

A) 240 B) 120
C) 210 D) 420
 
Answer & Explanation Answer: D) 420

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Q:

For the figure given below, find the value (in degrees) of 2∠A + ∠B.

A) 180° B) 202.5°
C) 250° D) 279°
 
Answer & Explanation Answer: B) 202.5°

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Q:

The external and the internal radii of a hollow right circular cylinder of height 15 cm are 6.75 cm and 5.25 cm respectively. If it is melted to form a solid cylinder of height half of the orignal cylinder, then the radius of the solid cylinder is

A) 6 cm B) 7.25 cm
C) 6.5 cm D) 7 cm
 
Answer & Explanation Answer: A) 6 cm

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Q:

The length and breadth of a rectangular piece of a land are in a ratio 5:3. The owner spent Rs. 6000 for surrounding it from all sides at Rs.7.50 per metre. The difference between its length and breadth is

A) 50 metres B) 100 metres
C) 150 metres D) 250 metres
 
Answer & Explanation Answer: B) 100 metres

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