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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 tank is 25 m long, 12 m wide and 6 m deep. The cost of plastering its walls and bottom at 75 paise per sq. m, is:

A) Rs. 456 B) Rs. 458
C) Rs. 558 D) Rs. 568
 
Answer & Explanation Answer: C) Rs. 558

Explanation:

Area to be plastered= [2(l + b) x h] + (l x b)

= [2(25 + 12) x 6] + (25 x 12)  

= (444 + 300)  

= 744 

 

Cost of plastering = Rs. 744 x (75/100)= Rs. 558

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1 5260
Q:

The volume of a hemisphere is 89.83 cm³. Find its diameter (in cm).

 

A) 3.5 B) 7
C) 14 D) 10.5
 
Answer & Explanation Answer: B) 7

Explanation:
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0 5133
Q:

One side of a triangle has length 8 and a second side has length 5. Which of the following could be the area of the triangle?

A) 24 B) 20
C) 26 D) 34
 
Answer & Explanation Answer: B) 20

Explanation:

The maximum area of the triangle will come when the given sides are placed at right angles. If we take 8 as the base and 5 as the height the area = ½ x 8 x 5=20

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Exam Prep: GRE

2 5109
Q:

The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 8 minutes, then the area of the park (in sq. m) is:

A) 15360 B) 153600
C) .30720 D) 307200
 
Answer & Explanation Answer: B) 153600

Explanation:

Perimeter = Distance covered in 8 min. = (12000/60) * 8 = 1600m 

Let length = 3x metres and breadth = 2x metres.  

Then, 2(3x + 2x) = 1600 or x = 160.  

Length = 480 m and Breadth = 320 m.

Area = (480 x 320) = 153600 

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0 4962
Q:

Ratio between heights of two cylinder in the ratio 3:5. Their volumes are in the ratio 27:80. Find ratio between their radius ?

A) 1:3 B) 2:1
C) 3:4 D) 4:7
 
Answer & Explanation Answer: C) 3:4

Explanation:

bank

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14 4932
Q:

Which of the following option is CORRECT for SAS similarly criterion for the triangle ABC and DEF?

 

 

A) B)
C) D) All options are correct
 
Answer & Explanation Answer: D) All options are correct

Explanation:
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0 4909
Q:

Calculate the number of bricks, each measuring 25 cm x 15 cm x 8 cm required to construct a wall of dimensions 10 m x 4 m x 5 m when 10% of its volume is occupied by concrete ?

A) 6000 B) 5400
C) 3800 D) 4700
 
Answer & Explanation Answer: A) 6000

Explanation:

Let 'B' be the nuber of bricks.

=> 10 x 4/100 x 5 x 90/100 = 25/100 x 15/100 x 8/100 x B

=> 10 x 20 x 90 = 15 x 2 x B

=> B = 6000

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5 4903
Q:

The difference between the length and breadth of a rectangle is 23 m. If its perimeter is 206 m, then its area is:

A) 1520 sq.m B) 2420 sq.m
C) 2480 sq.m D) 2520 sq.m
 
Answer & Explanation Answer: D) 2520 sq.m

Explanation:

We have: (l - b) = 23 and 2(l + b) = 206 or (l + b) = 103. 

Solving the two equations, we get: l = 63 and b = 40. 

Area = (l x b) = (63 x 40) sq.m

= 2520 sq.m

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1 4900