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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:

A cone is hollowed out of a solid wooden cube of side 6 cm. The diameter and height of the cone is same as the side of the cube. What is the volume of the remaining cube?

A) 159.42 cubic cms B) 323.15 cubic cms
C) 106.33 cubic cms D) 210.66 cubic cms
 
Answer & Explanation Answer: A) 159.42 cubic cms

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Q:

What is the slope of the line perpendicular to the line passing through the points (­6,3) and (2,7)?

A) -2 B) 2
C) 1/2 D) -1/2
 
Answer & Explanation Answer: A) -2

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Q:

If the circum radius of the equilateral triangle is 12 cm then what is the value of in radius (in cm) of the triangle?

A) 3 B) 6
C) 8 D) 10
 
Answer & Explanation Answer: B) 6

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Q:

D and E are points on side AB and AC of ΔABC. DE is parallel to BC. If AD:DB = 2:3, what is the ratio of area of ΔADE and area of quadrilateral BDEC?

A) 4 : 21 B) 4 : 25
C) 4 : 29 D) 4 : 9
 
Answer & Explanation Answer: A) 4 : 21

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Q:

The point of the intersection of three medians is known as the ____________.

A) circum-centre B) in-center
C) centroid D) orthocenter
 
Answer & Explanation Answer: C) centroid

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Q:

The heights of a cone and a cylinder are equal. The radii of their bases are in the ratio 2:1. The ratio of their volumes is:

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

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Q:

Two circles touch each other externally. The distance between their centres is 7 cm. If the radius of one circle is 4 cm, then the radius of the other circle will be

A) 3 cm B) 4 cm
C) 5.5 cm D) 3.5 cm
 
Answer & Explanation Answer: A) 3 cm

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Q:

If the curved surface area of a right circular cone is 10010 sq cm and its radius is 35 cm, find its volume?

A) 6930 cubic cm B) 13860 cubic cm
C) 3465 cubic cm D) 27720 cubic cm
 
Answer & Explanation Answer: B) 13860 cubic cm

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