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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:

Δ ABC is right angled at B. If m∠A = 30°. What is the length (in cm) of AB, if AC = 8 cm?

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

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1 1124
Q:

The curved surface area and the diameter of a right circular cylinder are 352 cm² and 14 cm respectively. Find its height (in cm).

A) 9 B) 8
C) 10 D) 11
 
Answer & Explanation Answer: B) 8

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1 1124
Q:

G and AD are respectively the centroid and median of the triangle ΔABC.The ratio AG:AD is

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

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0 1121
Q:

In ΔPQR, ∠QPR = 45° and the bisectors of ∠PQR and ∠PRQ meets at O. What is the value (in degrees) of ∠QOR?

A) 107.5 B) 112.5
C) 117.5 D) 122.5
 
Answer & Explanation Answer: B) 112.5

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2 1120
Q:

A cylindrical capsule has hemispherical ends of the radii equal to radius of the cylindrical part. If length of the capsule is 40 m and radius 6 m, what is the total surface area of this capsule?

A) 3017.14 sq mts B) 4525.71 sq mts
C) 1508.57 sq mts D) 754.29 sq mts
 
Answer & Explanation Answer: C) 1508.57 sq mts

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0 1119
Q:

The height and the total surface area of a right circular cylinder are 4 cm and 8π sq.cm. respectively. The radius of the base of cylinder is

A) (2√2 - 2) cm B) (2 - √2) cm
C) 2 cm D) √2 cm
 
Answer & Explanation Answer: A) (2√2 - 2) cm

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0 1118
Q:

In the given fig, ST||RP, then what is the value of supplementary angle y (in deg)?

A) 10 B) 60
C) 100 D) 170
 
Answer & Explanation Answer: C) 100

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0 1115
Q:

D and E are points on side AB and AC of ΔABC. DE is parallel to BC. If AD:DB = 2:5 and area of ΔADE is 8 sq cm, what is the ratio of area of ΔADE: area of quadrilateral BDEC?

A) (4:45) B) (45:4)
C) (8:45) D) (45:8)
 
Answer & Explanation Answer: A) (4:45)

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