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 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 = (πrl)sq.units 

 

4. Total surface area = (πrl+πr2)sq.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 set of three sides can't form a triangle?

A) 5 cm, 6 cm, 7 cm B) 5 cm, 8 cm, 15 cm
C) 8 cm, 15 cm, 18 cm D) 6 cm, 7 cm, 11 cm
 
Answer & Explanation Answer: B) 5 cm, 8 cm, 15 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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0 804
Q:

The volume of a right circular cone, whose radius of the base is same as its altitude, and the volume of a sphere are equal. The ratio of the radius of the cone to the radius of the sphere is

 

A) 33 : 23 B) 2 : 1
C) 1 : 1 D) 43 : 1
 
Answer & Explanation Answer: D) 43 : 1

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Q:

In ΔABC, the medians AD and BE meet at G. The ratio of the areas of ΔBDG and the quadrilateral GDCE is

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

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0 803
Q:

The ratio of total surface area and volume of a sphere is 1 : 7. This sphere is melted to form small spheres of equal size. The radius of each small sphere is 1/6th the radius of the large sphere. What is the sum (in cm2) of curved surface areas of all small spheres?

A) 31276 B) 36194
C) 25182 D) 33264
 
Answer & Explanation Answer: D) 33264

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0 803
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:

The length of one side of a rhombus is 41 cm and its area is 720 sq.cm. What is the sum of the lengths of its diagonals?

A) 82 cm B) 90 cm
C) 98 cm D) 80 cm
 
Answer & Explanation Answer: C) 98 cm

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Q:

The total surface area of a hemisphere is 41.58 sq cm, find its radius.

A) 4.2 cm B) 0.7 cm
C) 1.05 cm D) 2.1 cm
 
Answer & Explanation Answer: D) 2.1 cm

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