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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:

In a triangle ABC, AD is angle bisector of ∠A and AB : AC = 3 : 4. If the area of triangle ABC is 350 cm2, then what is the area (in cm2) of triangle ABD?

A) 150 B) 200
C) 210 D) 240
 
Answer & Explanation Answer: A) 150

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Q:

A regular square pyramid has side of its base 20 cm and height 45 cm is melted and recast into regular triangular pyramids of equilateral base of side 10 cm and height 10√3 cm. What are the total numbers of regular triangular pyramid?

A) 24 B) 20
C) 27 D) 28
 
Answer & Explanation Answer: A) 24

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Q:

In ΔABC, ∠B=90 deg and BC= √3 AB. Find the measurement of ∠A

A) 45 deg B) 90 deg
C) 30 deg D) 60 deg
 
Answer & Explanation Answer: D) 60 deg

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Q:

Which of the following is not true for a rhombus?

A) All sides are congruent B) Opposite sides are parallel
C) Diagonals are equal D) Diagonals bisect each other at right angles
 
Answer & Explanation Answer: C) Diagonals are equal

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Q:

Smaller diagonal of a rhombus is equal to length of its sides. If length of each side is 6 cm, then what is the area (in sq.cm) of an equilateral triangle whose side is equal to the bigger diagonal of the rhombus?

A) 18√3 B) 27√3
C) 32√3 D) 36√3
 
Answer & Explanation Answer: B) 27√3

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Q:

Length of the sides of a triangle are a, b, c respectively. If a2 + b2 + c2 = ab +bc + ca then the triangle is

A) isosceles B) equilateral
C) scalene D) right­-angled
 
Answer & Explanation Answer: B) equilateral

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Q:

The radius of a cylindrical milk container is half its height and surface area of the inner part is 616 sq.cm. The amount of milk that the container can hold, approximately, is [ Use : √5 = 2.23 and π = 22/7 ]

A) 1.42 litres B) 1.53 litres
C) 1.71 litres D) 1.82 litres
 
Answer & Explanation Answer: B) 1.53 litres

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Q:

A point P lying inside a triangle is equidistant from the vertices of the triangle. Then the triangle has P as its

A) Centroid B) Incentre
C) Orthocentre D) Circumcentre
 
Answer & Explanation Answer: D) Circumcentre

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