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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:

Find the total surface area (in cm²) of a right circular cylinder of diameter 28 cm and height 12 cm.

 

A) 2200   B) 2080
C) 1920 D) 2288
 
Answer & Explanation Answer: D) 2288

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Q:

The sum of the lengths of the edges of a cube is equal to half the perimeter of a square. If the numerical value of the volume pf the cube is equal to one-sixth of the numerical value of the area of the square, then the length of one side of the square is

A) 31.5 units B) 36 units
C) 27 units D) 18 units
 
Answer & Explanation Answer: B) 36 units

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Q:

The perimeter and the length of one of the diagonals of a rhombus is 26 cm and 5 cm respectively. Find the length of its other diagonal (in cm).

 

A) 6 B) 12
C) 24 D) 18
 
Answer & Explanation Answer: B) 12

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Q:

If the angles of a triangle are in the ratio of 2 : 5 : 8, then find the value of the smallest angle.

A) 36 deg B) 18 deg
C) 12 deg D) 24 deg
 
Answer & Explanation Answer: D) 24 deg

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Q:

If DE is parallel to BC and bisects the other two sides of the triangle ABC such that the ratio AD/DB = 5/13 and the length of the part EC is 26 cm. Then determine the length of AE (in cm).

A) 5 B) 10
C) 15 D) 20
 
Answer & Explanation Answer: B) 10

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Q:

In a triangle, one of the angles is three times the smallest and another is two times the smallest angle. Calculate the smallest angle.

 

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

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Q:

___ is the point at which the perpendicular bisectors of the sides meet and the center of the circle that circumscribes the triangle is ____.

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

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Q:

In ΔPQR measure of angle Q is 90 deg. If tanP = 24/7, and PQ = 14cm, then what is the length (in cm) of side QR?

 

A) 50 B) 20
C) 26 D) 48
 
Answer & Explanation Answer: D) 48

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