Area and Volume Questions and Answers

Exercise


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Q 1

A total of x feet of fencing is to form three sides of a level rectangular yard. What is the maximum possible area of the yard, in terms of x?


A)  

x²/9

B)  

x²/8

C)  

x²/4

D)  


Correct Option - B

Explanation

x feet of fencing covers three sides.

x = 2l + b

b = x-2l

Area of the yard

= lb square feet

= l(x-2l)

= lx - 2l²

To get the maximum possible value for the area,

d(area)/dl = 0

x - 4l = 0

l = x/4

The maximum value for area occurs when l = x/4

b = x-2l = x/2

Area

= (x/4)(x/2)

= x²/8

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Q 2

If each of the sides of a rectangle are increased by x units. Find the increase in the area.


A)  

lb+x(l+b)+x²

B)  

lb+x(l+b)

C)  

 x(l+b)+x²

D)  

4x


Correct Option - C

Explanation

Area of the rectangle

= (l+x)(b+x)

= lb+x(l+b)+x²

Increase in area

= x(l+b)+x²

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Q 3

One side of a rectangular field is 8m and one of its diagonals is 17m. The area of the field is


A)  

170m²

B)  

136m²

C)  

15m²

D)  

120m²


Correct Option - D

Explanation

√(l²+b²) = 17

l²+b² = 289

l² = 289-64 = 225

l = 15m

Area = 15*8 = 120 m²

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Q 4

A circular swimming pool is surrounded by a concrete wall 4 feet wide. If the area of the wall is 11/25 of the area of the pool, then the radius of the pool in feet is


A)  

24 feet

B)  

22 feet

C)  

20 feet

D)  

14 feet


Correct Option - C

Explanation

Let the radius of the pool be r feet.

Area of the pool

= πr²

Area of the concrete wall

= π(r+4)² - πr²

= 8πr+16π

(8πr+16π) = (11/25)*πr²

200r+400=11r²

11r²-200r-400=0

Solving,

r=20

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Q 5

If the radius of a circle increases by x units, its circumference increases by


A)  

2πx units

B)  

2πr units

C)  

2π(r+x) units

D)  

2π units


Correct Option - A

Explanation

New radius 

= (r+x) units

New circumference

= 2π(r+x) units

Original circumference

= 2πr units

The circumference increases by 2πx units.

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Q 6

In a rectangular hall of length 12m and breadth 8m, the sum of the areas of the floor and the ceiling is equal to the sum of the area of the four walls. Find the height of the hall.


A)  

10m

B)  

5m

C)  

7.5m

D)  

4.8m


Correct Option - D

Explanation

2*12*8 = (2*12h) + (2*8h)

h = 4.8m

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Q 7

A 3 cm cube is cut into as many 1 cm cubes as possible. What is the ratio of the surface area of the larger cube to that of the sum of the surface areas of the smaller cubes? 


A)  

3:1

B)  

1:3

C)  

1:9

D)  

27:1


Correct Option - B

Explanation

Surface area of a 3 cm cube

= 6*3²

= 54 cm²

Surface area of a 1 cm cube

= 6*1²

= 6 cm²

No. of smaller cubes formed

= Volume of larger cube/Volume of smaller cube

= 3³/1³

= 27

Ratio

= 54/(27*6)

= 1:3

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