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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:

The perimeter and the breadth of a rectangle are 44 cm and 10 cm respectively. Find its area (in cm2).

A) 60 B) 240
C) 120 D) 180
 
Answer & Explanation Answer: C) 120

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Q:

Find length of the arc whose central angle is 90° and radius of the circle is 3.5 cm?

A) 11 cm B) 5.5 cm
C) 16.5 cm D) 22 cm
 
Answer & Explanation Answer: B) 5.5 cm

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Q:

An angle is greater than its complementary by 20°. What will be the measure of the angle?

A) 55° B) 35°
C) 100° D) 80°
 
Answer & Explanation Answer: A) 55°

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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 two sides holding the right-angle in a right-angled triangle are 3 cm and 4 cm long. The area of its circumcircle will be in sq.cm:

A) 6.25pi B) 6.75pi
C) 5pi D) 7pi
 
Answer & Explanation Answer: A) 6.25pi

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Q:

PT is a tangent to a circle with centre O and radius 6 cm . If PT is 8 cm then length of OP is

A) 10 cm B) 12 cm
C) 16 cm D) 9 cm
 
Answer & Explanation Answer: A) 10 cm

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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 tent is to be built in the form of a cylinder of radius 5 m surmounted by a cone of the same radius. If the height of the cylindrical part is 6 m and slant height of the conical part is 10 m, how much canvas will be required to build the tent? Allow 20% extra canvas for folding and stitching. (Take π = 22/7)

A) 829.72 sq mts B) 414.86 sq mts
C) 1244.58 sq mts D) 207.43 sq mts
 
Answer & Explanation Answer: B) 414.86 sq mts

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